Playing a sneaky character in Oblivion
I've found quite difficult to use a sneaky character mostly because it's quite impossible for me to avoid close combat.
What are the best strategies to 'one-shot' an enemy or to deal with a crowd?
Use dagger with a bow secondary, because they have x5 and x3 backstab damage multipliers when sneaking. (assign shortcuts for both sets)
Get some invisibility rings and robes (or enchant them) (but don't go over 90% invisibility), if your a low level get invisibility potions, this will allow you to avoid combat and sneak through dungeons.
Get night eye.
By invisibility I obviously mean chameleon invisibility.
If you get in trouble you can always drink an invisibility potion and escape.
I passed all of the guild quests and the main quest as a stealth character with a dagger.
I ended up getting some chameleon rings and robes which made me 100% invisible 
Here you can see me in a restricted area, notice how the guards ignore me.
(the sword is white because of some bugged weapon skin)
the game lost it's charm for me but it's certainly easier to play someone 100% sneaky
Other than that I suggest you get some chameleon rings and achieve around 90% invisibility which is pretty fun to play at and is significantly easier to deal with crowd's which also allows you to use the dagger stealth kill modifier (x5) which is better than the arrow one (x3). (
, the difficulty level was close to max, and the arrows were useless, so to experience one shot kills you could always reduce the difficulty)
night eye beats any torch or anything that is visible to others, although just setting the in-game brightness is very close to night eye so use that if your having trouble seeing in the dark.
one example is when I was doing a assassination mission on the countess of anvil, the game felt like a real stealth game then.
Good luck! and remember, challenge is what keeps the game fun, challenge and leveling up (and some stories)
p.s. Thieves Guild missions are the best.
For sneaking around and getting one-shot kills, I would recommend going bow. You get a bonus multiplier to damage if you are sneaking and nobody sees you. If you get your sneak skill high enough, you can just sneak through most dungeons and never have to deal with crowds of enemies. You also get the damage bonus in melee if the enemy doesn't see you, which I found I was able to get a lot of times when a single bow shot wouldn't kill it (just crouch up right behind them).
Magic is extremely effective for stealth characters.
The best strategy for crowds is to use a turncoat spell to turn them against themselves. e.g. Sneak in with Chameleon, hit a couple people in the crowd with a max Rally + Frenzy, then sit back and watch the fun.
Once the fighting starts, the NPCs will continue to kill each other long after the spell has worn off.
Adding onto nimbus's answer, I would add that you want to take advantage of anything which gives you the Chameleon effect. Invisibility doesn't help, because the first time you take an action (such as shooting), invisibility is over. I found Chameleon considerably more effective, when staying in sneak mode. So increase your sneak skill as much as possible, and brew up as strong (and as many) chameleon potions as possible. If you can enchant, enchant your armor (preferably light armor) or clothing with chameleon.
With a high enough chameleon effect, and a 100 sneak, you can pretty much sneak around right in front of most NPCs.