Olaf does naturally beat Jax. What you can do is:
- ask for ganks. Since Olaf uses his Axe(Q) to do dmg, he pushes the lane and can get ganked (pre lvl 6)
- Go for Phage first. One Patch ago, I would have suggested you to go for HoG, but since it got nerfed I wouldn't recommend that. Try to get 2-3 Dorans Blades and then go straight for Phage -> Sheen.
- Max W (as always). Try to make the trades longer. Olaf has really really strong trades as long as they are short, since his main dmg is his E. You have to know the CD on his E. You can just eat one E, than activate your stun and chase him down for several seconds (~5). After you stunned him and did 1 -2 hits (obviously using W, Q if necessery to gap close) you can just back out, or if you have Q up jump away.
- Healpots and a red Elexier. Use the red elexier to make him overextend, after lvl 6 if noone has an advantage you will probably be stronger.
its just a bad match up for Jax, but if you play deffensive and leave the lane with 10-20 cs less, you are still going to do work in teamfights.
Rammus' great strength comes with the element of surprise. If Rammus isn't in your face, and he isn't powerballing, then he's not scary.
First, the general Powerball gank-tip: start charging it before you actually go in to gank. It takes some time to get spinning, but lasts for quite awhile. If you just press Q and charge on in, you give your opponent precious escape-time. Figuring out the timing on this is critical.
Second, wards. Namely, destroying their's. Rammus late-game can be something like Fiddlesticks; if you can get the jump on them from a surprising position, you've really got something. Have an oracle's on your team (either you or your support) and clear out those wards. Leave them guessing.
Third, scaling MR blues. Rammus needs MR, and these provide a healthy chunk.
Fourth, effective team communication. When Rammus goes in, he goes in. He isn't getting back out. If your team is not prepared to jump in after you, you're going to have a bad time.
Fifth, make use of your early-game advantage. Rammus is FRIGHTENING during the laning phase. If you manage your Powerball correctly, and your lanemate has any CC at all, you're pretty much guaranteed a kill. Gank frequently.
Sixth, give your lanemates the kills, whenever and wherever possible. Don't ever let a kill get away, but if the opponent is certain to drop, give it to your lanemate. They can put that extra gold to much better use.
Best Answer
Jungle vs Laning
Olaf can jungle or lane. I prefer to jungle but arguments can be made for both sides.
If you are going to jungle here are some good stating items: Cloth armor + potions OR Regrowth Pendant and 1 health potion or vampiric scpeter (not recommended). Cloth armor will build into a Madred's Razor and then Wriggle's Lantern (Bloodrazor is unnecessary and i will explain why in a moment). Regrowth Pendant will build into a Warmog's Armor. Warmogs gives you a lot of bonus health and health regen. Olaf's Viscous Strikes grant him 1% of his max health as additional damage so you also get some damage from this item. What is more interesting is how additional health works with Olaf's innate ability Berserker Rage. As he loses health he gains attack speed on a 1 to 1 ratio (1% health loss = 1% increased attack speed). Which route you take (and these arent the only ones) is up to you and what you need to accomplish. Do you need to be more of a tank or deal more damage? Your build will change from there.
The important abilities when jungling are Viscous Strikes (level 1) and Undertow. Generally Viscous Strikes stays at level 1 for quite some time as the benefits from Reckless Swing and Undertow are greater. Undertow increases your dps and Reckless Swing significantly increases your damage to Champions (which is important when you gank as a jungler).
In a lane Undertow is probably your best ability as it lets you harass and chase enemy champions. Reckless Swing is also a key ability as no one will be able to trade damage with you at close range and come out ahead since Reckless Swing deals true damage.
Ganks and Team Fights
Olaf really likes attack damage and health items (attack speed and lifesteal are also good). As such, Youmuu's Ghost blade, Frozen Mallet, Randuin's, Stark's Fervor, Wriggle's Lanter, Black Cleaver, Warmog's and Berserker Boots are all excellent choices. Take note that Olaf is completely incapable of dealing magic damage or using ability power (unless he picks up a proc item like malady, wits end, bloodrazor, executioner's calling, sword of the divine) and as such it is not advised to spend the gold on items that grant ability power. His ult provides 30 armor penetration (passively at ability level 3) and as such attack damage, attack speed and additional armor pen (if required) go a long way. Life steal is granted by his Viscous Strikes ability but it doesn't hurt to pick up some more.
The key to playing an effective Olaf is doing nothing half way. If you are in a team fight you are in it until you die or they die. Olaf's survivability is directly related to the damage he is outputting as a result of his innate attack speed bonus (as he takes damage) and his lifesteal (enhanced by his armor penetration and attack speed). Running away is often futile and will get you killed as Olaf doesn't really have an escape mechanism. This is actually why I prefer Smite and Flash/Ghost when jungling and Ghost and Flash while laning. 1v1 is really no different. If you find yourself on the run it is often best to turn and fight if you aren't making progress as Viscous Strikes also gives you spell vamp which helps with Undertow and Reckless Swing. Don't forget Reckless Swing deals TRUE damage so it isn't effected by armor or magic resist.
Runes
Marks should be Armor Penetration/Attack Speed (I really think Armor Penetration is the way to go but arguments can be made for both).
Seals should be armor or dodge as they increase your survivability and you dont really need a lot of magic regeneration (which is generally the other seal I find most useful).
Glyphs can be Flat Magic Resist or Cooldown Reduction. I tend to take Flat Magic Resist with Olaf as his cooldowns aren't terribly long to begin with and Undertow cds faster when you pick up your axe anyway. Increased CDR really means more Reckless Swings and Ults but it really isn't necessary.
Quints can be Health (recommended) or Armor Penetration or a combination of the two. Health is genuinely useful early game and Olaf picks up enough Armor Penetration though the Marks, his ultimate and items that the health Quints are put to better use. You can argue for Gold/10 quints on a jungler but I don't think that is wise with Olaf.
Masteries
Masteries depend again on jungle/lane The Jungle masteries that I use might look a little odd but it works 11/9/10 Crit (3) and Smite (1), Attack speed (4), Armor Pen (3)/ Magic Resist (1) and Armor (3), Dodge (4), Nimbleness (1)/Perseverance (3) and Ghost (1), Xp Gain (4), Monster Buff Duration (2). If you aren't level 30 and you only have some masteries to pick from I would prioritize the utility tree then the offense tree then the defense tree but really you want to have most of the listed masteries and runes if you are going to jungle because they make a big difference.
The laning Masteries can be 21/9/0 or 11/29/0 or 21/0/9 21 in Offense is standard crit, attack speed, armor pen, bonus damage, crit damage, total damage in any case. For the 11/29 build you get to armor penetration at least.
The 29 to pick up in the Defense tree are armor and magic resist, dodge if you have dodge runes, nimbleness (if you have dodge) and flat damage reduction and health. Feel tree to pick up the extra attack speed bonus but the additional ability power it grants wont do you much good.
In the Utility tree you want to pick up Ghost and Regeneration, Experience Gain, and then gold or meditation or monster buff. For the good it does I would pick up 1 in Meditation as the monster buff duration would be going to your jungler or your AP carry and 1 gold in 10 isn't all that useful on Olaf. It is better to find yourself not mana starved.
Really long answer for what looks like a short question but I hope it helps.
I also encourage you to read guides for Olaf (or any champion you are starting to learn) to get a sense for what others recommend. Then play them out see what you like and make your own build. If you are going to jungle I suggest even more strongly to check out a guide specifically for that as the starting items and route through the jungle can be fairly specifically worked out to maximize profit.