[RPG] Why does the pre-gen Drow Rogue have a 0 Str modifier but a Strength score of 8

So, not to sound obvious, but multiclassing as a Druid will increase your versatility the most. The Druid is a full caster with a nice variety of offensive, defensive, and utility spells. As well as the healing you mention. 1 level of Druid would give you 2 cantrips and access to all 1st level Druid spells. 2 would give you Wild Shape, after that it's pretty much all just more spells.

Of the 3 Martial Archetypes, Champion doesn't increase versatility at all. It only makes you better at killing things.

Battle Master only makes you better at combat, but you do get access to a wide range of combat options. It would definitely increase your versatility within combat, just not outside of it.

Eldritch Knight is a bit more interesting - it slowly gives you spells. For the most part, they're restricted to Evocation and Abjuration, meaning that once again it mostly just increases your combat versatility. With that said, some Abjuration spells are useful for things other than killing, and careful selection of the few spells you get to choose freely can massively increase your out-of-combat utility.

So, the simplest option to increase your versatility would be to stick with Fighter and take Eldritch Knight. This could be done in conjunction with a single level of Druid to get all the 1st level Druid spells. The multiclassing rules on spell slots would work out in your favour here; for example, you could cast Cure Wounds out of your highest level spell slots.

If you really want to just boost your versatility, you should dump Fighter and go for Druid. That said, at that point your Fighter levels would be going to waste a bit. If you want to focus on Druid, you should definitely get either 4 or 6 levels of Fighter so that you don't lose an ability score increase.

In the end, you can mix and match Druid and Fighter levels however you want; but you should probably keep them in multiples of 4 so that you don't lose ability score increases. After that, it's just a matter of deciding which Druid or Fighter features you want and taking enough levels to get them.

As is the usual advice, I would say that talking to your DM and talking to your fellow players is a good place to start. Express your concern to your DM...he's the one who can help you with this, not us.

But, I don't think it's necessary just yet. You still have a significant role in the party.

A few points to consider...

1. The Bard was almost certainly going to surpass you in Intimidate if he took Proficiency in that skill. Bards are a Cha-primary class who, at high level, get access to the spell Glibness. Only they and Warlocks can cast that, and you simply can't compete with a guaranteed 15 or better on any Charisma roll. I mean...that's a major feature of Bards. Insane Social Skills. This doesn't mean you can't Help though. Be big, threatening, and intimidating. Loom behind the Bard's shoulder while he does the talking. Crack your knuckles or rub the haft of your axe at meaningful times...give that Bard Advantage on his check.
2. In terms of damage...yeah, Rogues do stupid amounts of single-target damage. That's kind of their whole schtick. But, in exchange, they are relatively fragile. Against a single target smacking them once a round, they are fairly good at not dying. But they'll go down like a chump against a mob of enemies. You won't. It's kind of a trade off. I mean...an angry 20th level Wizard can take out a significant portion of a city in a few rounds...but they are also made of glass. You don't hit quite as hard as the Rogue, but you hit hard enough to meaningfully contribute to the party's damage output, and you can get hit in the face a LOT MORE without going down.
3. You are still significantly better at Strength-related activity than the Rogue, unless he has Expertise in Athletics. As a Barbarian, you have Advantage on all Strength Checks that you make while Raging and, because of your 15th Level Persistent Rage, coupled with the Unlimited Rages of 20th level...you should be making every strength check with Advantage, simply by firing up your Rage before you attempt it. If you want to see the actual math, you can see it in this AnyDice Program. In it, I compare the Rogue's raw Strength Check with your Advantaged Strength Check (both at a +7 to their Strength Check). Their average roll is a 17.5, yours is 20.8. And with a narrower Standard Deviation, you will consistently churn out better results than the Rogue. (And if you took the 6th level Bear feature, you can carry/lift twice as much as they can without having to make a check at all)
4. The Rogue should probably always have been the infiltrator all along, even if he wasn't as good at climbing walls. Not being noticed is generally more important than getting over the walls in one attempt.
5. You are still, quite definitively, the party tank. You almost certainly have the most hit points, and since you should be perpetually raging while in combat, you have resistance to everything but Psychic Damage. And the 14th level Bear trait, coupled with Sentinel makes you fantastic at keeping enemies focused on you...so the comparatively fragile Rogue can hit them like a freight train. In the entire party...you're the one who can take a Dragon's breath weapon to the face and shrug it off without flinching.

Ultimately, your choices while leveling your character resulted in a character that is immensely hard to kill, and can probably throw a horse at someone they don't like, and rip the portcullis off a castle. And he's really good at keeping enemies focused on him. You're good at being scary....but being big and threatening only goes so far compared to the clever words of a Bard who can make all sorts of insinuations and suggestions that are far scarier than a big muscular guy. Or perhaps he just knows the right things to say to make you seem even scarier.

You have somewhat pigeonholed your character into this by your Feat selection, class build selection, and ASI choices and, truthfully, barbarians have a fairly narrow class focus anyway. A Bear Totem Barbarian's primary focus is "I'll keep their attention, they can't really kill me, you guys pummel them." As D&D is first and foremost a game focused on combat...the ability to keep enemy attention focused on the guy who is near-impossible to kill is a very valuable resource to bring to the team.

Seriously...just see how your fellow players feel about the prospect of going into combat without their favorite meat shield. Based on my prior experience with tanky characters....they'll think about all the damage you soaked for them...consider all that damage hitting their characters, and not like the idea one bit.