Hi, I'm doing a skooma overhaul, but I can't seem to figure out some way to make it so that the addiction effect will only take place after a certain amount of time. Any ideas?

Also, how to make it so that taking more skooma will disperse the addiction effects, and it will happen again after the time is up.

Use a skooma addiction "quest"
I say quest in quotes because you dont need stages so much as a script to track it. You just to need to increment a counter every time you drink a skooma then you can start adding effects when player reaches the addiction level
This should help get you started: http://www.creationkit.com/OnEquipped_-_ObjectReference