I recently finished a CoS campaign with a small, somewhat oddly-built party. As a module, Curse of Strahd does a pretty good job of keeping the pressure on with very little work from the DM. It's fairly easy to tweak encounters, although as a warning it is also not too hard for the PCs to wander off-track and bite off more than they can chew!
Aarakocra and Flying Players
For your specific example, I think Barovia is a fairly safe place to have a player be an Aarakocra. There are a lot of things you can bring in to make things easier.
Terrain
A lot of the valley is forested, and the forests are described as incredibly dense, twisted, dark, and foggy. Flying in there would likely be difficult if not impossible.
The forests are also, like everything else in the valley, an extension of Strahd's will: if it's narratively useful for the trees to claw our Birdman from the sky, they could.
As a side portion of terrain, there are a lot of indoor scenes where flying wouldn't put you meaningfully out of reach.
Enemies
Flying may not put you out of reach of your foes here. While some humanoids might not have a ranged weapon it would be easy enough to add one, and additionally, this is gothic horror with a vampire baddie. There are quite literally endless bats.
Perhaps more dangerously, Strahd and Bucephalus can fly as well.
There is also the Roc of Mount Ghakis, which I had planned to have chase any PC that got too high up. I viewed this "Fly too high, attract the big fish" mechanic as a way to prevent reprisal-free fireballs from 200' by a flying sorcerer.
Weather
Barovia's weather is miserable. It's always overcast, often rainy, and storms are common. Flying in a rainy windstorm sounds like a great way to let the DM move you every turn. Lightning is a very real thing that I'd totally have intersect with a 150 lb chainmail-wearing bird on its way to the ground.
But really, the number one in my mind is: unless this is formal AL play (since they ban L1 Aarakocra anyways), don't worry about it too much! As this excellent answer on flying PCs explains, it is often a self-limiting feature that you as the DM should be aware of, but not worried about.
General Class Balance
I had a party of largely Unearthed Arcana multiclasses, and found it balanced out pretty well. Honestly, for a group going into a campaign with a known vampire big bad in it, they went pretty light on the Divine magic.
With one exception (see spoiler), I didn't see any combo in-game or during spitballing sessions with my players that would seriously de-fang anything in the game. Be sure to pay attention to action economy and estimated encounter difficulty, and you should be fine.
The one exception: Strahd himself. The climactic fight is written to be largely party-vs-Strahd. He's relatively tough and hits hard, but he's losing in action economy and the Sunsword will remove a lot of powers and cause him serious harm.
I found you need to play him very carefully and very smart. But remember: he's a master strategist and has been spying on the party via his animal and human servants, and with Scry.
The curse affects the character immediately, but they might not necessarily be aware of it at first (or even for quite some time)
From the Lycanthropes section of the Monster Manual, p. 206 (non-italic bold emphasis mine):
Curse of Lycanthropy. A humanoid creature can be afflicted with the curse of lycanthropy after being wounded by a lycanthrope [...]
A lycanthrope can either resist its curse or embrace it. By resisting the curse, a lycanthrope retains its normal alignment and personality while in humanoid form. It lives its life as it always has, burying deep the bestial urges raging inside it. However, when the full moon rises, the curse becomes too strong to resist, transforming the individual into its beast form—or into a horrible hybrid form that combines animal and humanoid traits. When the moon wanes, the beast within can be controlled once again. Especially if the cursed creature is unaware of its condition, it might not remember the events of its transformation, though these memories often haunt a lycanthrope as bloody dreams.
From the parts I've emphasised above, it seems that, although a character afflicted by lycanthropy might feel that something is off, feeling "bestial urges raging inside it", it is still entirely possible for the character to be "unaware of its condition", even after transforming during a full moon.
(I'm assuming that a character who is unaware has no choice but to resist the curse; there's some stuff about embracing the curse, but surely you have to know about it first? I'm making an assumption that embracing the curse is only an option to a character that has become aware of it in the first place. See this Q&A for more info.)
Furthermore, the sidebar on p. 207 implies that the changes to the creature's stats happen immediately since no time frame is given between failing the saving throw and being considering cursed (which matches up with the lack of a time frame given in the wording of "afflicted with the curse of lycanthropy after being wounded by a lycanthrope", from the above quote), so although the character wouldn't necessarily be aware, the player almost certainly will be.
How to rule this in your specific example
Depending on how you think such things would go down at your table (you know your players better than us), you could either just flat out tell your player, but remind them that their character doesn't necessarily know (or maybe you decide that the character does "just know"? Up to you and your player...), or you could try to hide it from the player and let them figure it out over time.
(Given that the werewolf ability score increase is for Strength, and I'm assuming your paladin player already has a decent Strength score, you can ignore that bit, making this more plausible to do than if, say, a wizard PC got cursed by a werewolf; the player would probably want to update their Strength score straight away if that were the case, which would prevent you from hiding it from them).
For example, when they roll perception checks, give them advantage (because of a werewolf's Keen Hearing and Smell trait) but don't tell them why. Remember that they have immunity to non-silvered, nonmagical weapons when rolling for damage when you hit them, and telling them that they take no damage, but without an explanation. And perhaps tell them that they occasionally feel whatever you interpret "bestial urges raging inside" them to mean (although they can choose to do nothing with that, just tell them that they feel it).
At the point where the player figures out what's going on, you can then talk to the player about roleplaying their character not knowing about it, or figuring it out, or whatever else would be the most fun for the player/table. Of course, given that your player pretty much knows exactly what that failed saving throw meant, you're probably better off just telling the player upfront and deciding with them whether it would be more fun to have the character know, or to have the character not know and have to slowly figure it out.
An aside about changing alignment
I also want to remind you that the character's alignment will only change if the character embraces the curse, as outlined in the sidebar on p. 207:
If the character embraces the curse, his or her alignment becomes the one defined for the lycanthrope.
However, on p. 206, it states:
By resisting the curse, a lycanthrope retains its normal alignment and personality while in humanoid form.
So I'm guessing that someone resisting the curse cannot voluntarily shapeshift (see this Q&A for more info), and that they are not themselves (and therefore, not their normal alignment) when they are forcibly shapeshifted during a full moon (which fits the flavour, at least). Just something to bear in mind (and possibly something you might need to make a ruling on...)
Best Answer
Use weapons which can hurt lycanthropes
In humanoid or hybrid form, lycanthropes can use weapons. If they are expecting to get into a fight with other lycanthropes, they would acquire weapons which can harm lycanthropes (in the same manner than non-lycanthropes would acquire weapons which can harm lycanthropes). Silvered or magical weapons are the obvious choices. Torches, since they deal fire damage, are good if proper weapons are not available.
Such weapons might be difficult to acquire and would be closely guarded by their owners, but if a fight with a lycanthrope is likely then it would be advantageous to have such weapons.
If any of the lycanthropes are spellcasters, they could attack their enemies with damaging spells. Magic weapon, if available, can allow a spellcaster's allies to also deal magic damage.
Poisons, if you can deliver them, can harm a lycanthrope. Injury poisons won't be much good unless you have a silvered or magical weapon, but inhalation or contact poisons are usable in combat and would work against lycanthropes. Ingested poisons would also work if you can manage to force-feed it to your target. However, poisons typically are rather expensive, so it may be hard to get enough for a full brawl.
Vials of acid or alchemist's fire are also options, albeit expensive ones.
Wrestle them into hazards (falling, suffocation, fire)
Falling deals bludgeoning damage but is not an attack, so lycanthropes take falling damage normally. To use this strategy, you need to either be able to fly or have a something at least 10 feet tall to push your enemies off.
Suffocation (PHB 183) can also kill lycanthropes. Forcing them underwater or strangling them would achieve that goal. In an evenly matched fight this strategy is unlikely to be viable, but if one side outnumbers the other (perhaps by picking off members one by one) then they could all work to restrain a target then either hold them underwater or choke them to death. The aggressor would need to hold this position for the full amount of time needed to drop the victim to zero hit points for it to have any effect.
There is no strict rules-as-written method for an arbitrary creature to cause another creature to choke. Bearing in mind that the rules of D&D 5e do not cover every possible action, strangling or choking would fall under Improvising an Action (PHB 193, sidebar). I'd point you to the Ettercap variant Web Garrote (MM 131) for a suggestion of one method to strangle a foe which can be easily adapted to a weapon which other creatures can use.
If you are uncomfortable with this kind of improvisation, it is still possible to drown an enemy by strict rules as written. Grapple an opponent then knock them prone in a body of water which is deep enough to immerse a prone lycanthrope but not a standing one. If the aggressor can securely restrain the victim, such as by tying them up, all the better. If the victim can be held there for a few minutes, they will drown.
Fire can hurt lycanthropes. While torches do a measly one fire damage, if you can shove a lycanthrope into a bonfire, or douse them in oil and set them alight, you would do a lot more damage.
It should be noted that, regarding traps which deal bludgeoning, piercing or slashing damage, some involve attack rolls (swinging blades and darts traps normally fall into this category), so would not harm a lycanthrope, while some do not require an attack roll (such as falling rocks or spiked pits or caltrops).