PC Sneak animations are messed up

My Skyrim is latest stable version (v1.5.xx)
Ever since installing these four mods:
- Bow running animation: http://skyrim.nexusmods.com/mods/16975
- Perk up: http://skyrim.nexusmods.com/mods/9359
- Perk points potion: http://skyrim.nexusmods.com/mods/10836
- Uncapper: http://skyrim.nexusmods.com/mods/1175
My character's sneak animations are all messed up. For example, sneak forward now plays the sneak right animation, sneak backwards now plays the sneak forward animation, sneak diagonal up-left now plays the sneak roll animation (sneak + sprint), sneak draw bow now plays the sneak fire arrow animation, and sneak sword attack now has no animation (game simply freezes for a second for the "blank" animation), etc. All other animations like walking and running and attacking while walking/running are fine.
I have removed every single file associated with those four mods, including esp's, hkx animation files, ini's and script files, but the problem is still not fixed. If I choose to continue latest save game, the sneak animations are already messed up upon starting game. If I choose to continue an earlier save (a save made prior to adding those 3 mods), at first sneak animations will appear normal, however the moment I enter another area via loading screen like through a door or something, sneak animations are immediately messed up.
I have no idea why this is happening because those mods I installed have nothing to do with sneaking. I have not touched any of the .bsa package files at all. The only theory I have is something is messing up the way the Skyrim - Animations.bsa package is read, eg assigning "sneak_forward.hkx" as the sneak backwards animation or something.
Does anyone know how I could fix this, without reinstalling the game? I got lots of mods installed and really don't want to start over.

Deactivate each mod one by one and see which one changes gameplay. If it doesn't work, it may be more than one causing the problem.

I've already completely deleted those 4 mods I installed. The problem only started occurring after installing those 4 mods. But it seems one of the 4 mods permanently damaged the game. It reminds me of the "better horses" mod, that mod permanently messes up the horse-mounting animation even after complete uninstall.
Edit: I have unactivated every single mod through NMM. The problem is still there. =/
Then it must be one of the mods added/removed/changed some animations file without me knowing. >_<

If you read the mod notes, they will often suggest backing up the files they are replacing and clearly identify which ones you should copy.

The 1.6 patch breaks many animation mods so you should steer clear of them until the mod creator has confirmed they have updated their mod to work with 1.6. In the meantime you should reinstall the game to restore any data lost to the mods.