So, effects of warp? They run a range from "lol" to "OMG AZANOR WHYYYY". Basically, every few ticks, you have a chance of something happpening. The higher your warp, the more likely something is to happen. At lower warp, you'll get less events and they'll generally be pretty harmless. At high levels, you'll get a lot more events and they can be much more annoying/dangerous.
At lower levels, you'll occasionally get things like spoooooky vision shaders, or your character will hear whispers in his ear and get free research points. You'll occasionally get messages saying something's behind you, but nothing will be there...
At mid levels, you'll start seeing various status effects. Some status effects are:
Thaumaria - Your character poops little flux goo puddles. More silly/annoying than actually harmful.
Flux Flu - Your vis efficiency goes down, making everything cost more vis than normal.
Flux Phage - Like Flux Flu, but contagious, so you can spread it to other players. Achoo!
Sun Scorned - Screen gets unbearably bright and sunlight burns your character
Deadly Gaze - Anything you look at gets hurt. Try not to stare at your friends.
Unnatural Hunger - You feel hunger effects and the only way to get sustenance is to eat rotten flesh or zombie brains.
At higher levels, the interesting stuff starts happening. If your warp is high enough, you may get attacked by swarms of mind spiders. The mind spiders are only in your head, so they won't do any damage and they only have 1 HP each.
At the highest levels, everyone's favorite buddies start visiting you. You'll get a message about shapes in the fog and the game will suddenly get really foggy as though you have draw distance at minimum. Eldritch Guardians will spawn around you and attack you. Unlike the mind spiders, the guardians are NOT figments of your imagination and can seriously wreck you if you're not equipped to handle them. By the time you've gotten this much warp, you've probably unlocked a lot of powerful research already, so it shouldn't be too much of an issue unless you were extremely reckless with eating zombie brains and crafting flesh golems.
You can prevent Warp effects from happening to you by using Bath Salts. Every time you take a fancy bath with the bath salts, you gain the Warp Ward status effect. Warp Ward prevents any warp effects from happening while you have it. If you have low warp when taking a bath, Warp Ward will last half an hour or maybe more when using it. At higher warp levels, Warp Ward duration gets shorter and shorter.
If you just muscle through the warp effects, they'll eventually start to wind down in frequency and then stop happening altogether as long as you don't do anything to give yourself more warp.