Edit: Ugh, meant to post in cheats/hints/spoilers. Edit: Moved, thanks mod.
Apologies, I did report it immediately after submitting so should be moved or deleted.
1. Enchanting. Everyone knew this would be here and I'm getting it out of the way. 2 enchants can = 4 perks in a combat tree. 4 can give completely free spells from a school. Can reach resist magic cap relatively easily. Any skill you want to be effectively twice as good at? Enchants can do that. It can get better with alchemy, but doesn't even need it to be overpowered really. It's also easy money especially when banish is acquired.
2. Alchemy. Even without the alchemist/enchant loop, one can still chug practically limitless health potions and/or potions of extremely high damage boosts to combat skills and/or resists or health boosts to become essentially invincible until they run out - unless an enemy can one shot them, which even on legendary isn't likely if you're in decent gear and taking precautions with pre-emptive potions. And like enchant, it's easy money.
3. Barbas. Barbas is a follower, and often a rather annoying one at that. But he has one particular, somewhat redeeming trait that makes him the most powerful follower by a landslide though. Barbas is literally invulnerable, meaning instead of just kneeling for awhile when brought to a point near death like other followers, enemies will just indefinitely attack him to no effect. You can let him pretty much tank anything in the game while you shoot or blast them from safety. The masque of clavicus vile isn't that great anyway.
4. Conjure Dremora Lord. "I SMELL WEAKNESS". The most powerful, badass thing that you can summon. While not that durable, they deal serious damage which is not affected by difficulty level because, like the other inferior summons, they're playing by NPC rules not the player's, and you can have two of them out at the same time. I imagine you could handle any difficulty with this spell if you just stayed out of the way and let them handle things, and had a decent armor with some resist enchants to be safe.
5. Necromage + Vampire. Basically, a 25% strength, 50% duration boost to a remarkably long list of things including spells, enchants, potions, even perks. With dawnguard, being a stage 4 vampire is no big deal and there's no reason to not to be one if your goal is power(although stage 1 is better, it can be tedious feeding so I don't bother). Offsetting its weaknesses is easy, and the other vampire boosts aren't bad either - nice to be able to affect things with pacify at high levels without needing dual casts. The duration boost alone feels so necessary for many spells that are annoying to recast, this is a staple for me since Dawnguard.
6. Smithing. Maybe you wonder why I put this so low, but it's because alchemy/enchant are what make it incredibly overpowered, without them it's only like...normal overpowered? Don't want to sink 5 perks for 100% armor boost? No need, smithing will let you hit the cap with a little help from his overpowered friends.
7. Soup. Well, vegatable soup as well as venisor and beef stew. I would assume most know power attacks and shield bashes only require 1 stamina. Well, you'll be able to spam them indefinitely with this. No need to put your level ups in stamina.
8. Dual Wielding. Theorycrafting has pretty much proved this to be the best damage by a landslide of any combat style. And it's not perk intensive - armsman and 2-3 perks is all you really need since the weapon type specific perks are utterly useless due to being based only on base damage of a weapon, and others require clunky/inefficient attack types to do anything and what they do isn't even all that spectacular. The speed of its attacks being based on the off hand adds a little extra cheesiness on top of the pile too - mace main hand + sword or dagger main hand being the ideal. And it works with dual dagger sneak attacks - though you're already at overkill without them probably.
9. Shields, of course with shield perk tree. There's some pure hilarity here. With soup - or even restoration + respite perk - you can basically stagger-lock many enemies with bashes, power bash letting you kill them whilst doing so. Then there's shield charge, where you knock things around with minimal stamina cost. And block runner is also amazing with some exploit potential. There are also some shields that add some incredible utility as well, most notable being the absolutely ridiculous aetherial shield which provides practically infinite crowd control. It's not necessary to bother with shields to become overpowered really, but at early levels on harder difficulties they can be the difference between life and death, while remaining an asset at high levels if you find dual wielding too boring and spammy.
10. Illusion. There comes a point when it's completely unnecessary, but if you want to play on master/legendary from the start, this is your safety net. The levels the spells effect do not change, nor are enemy levels changed, with the difficulty setting. So you can calm threatening enemies, use it spam sneak attacks, just get some outside-combat mana regen which is far faster than in combat regen, etc. Or, make enemies just fight eachother while you sit back and /popcorn.
List does not include things that are blatantly cheats, just taking advantage of intended game mechanics, and a few things they might've overlooked, in ways that are ... probably unintended but still - there's a line!