Generally, drugs effect vampires in much the same way they would humans.
Vampires can drink alcohol, and can get drunk. They've also been seen smoking cigarettes, which would be pretty pointless to use if the drug didn't effect them, though it could be argued that it could be for image or style. Vampires can also be effected by drugs in a person's blood stream, and might not feed off a person if the drug could have a bad effect (For example, Angelus did not drink from a student who had taken a drug which later caused the student to turn into a fish monster.) My guess would be that vampires would recover from the effects of drugs sooner, as they have enhanced healing powers, but that is just a big guess.
Heavy poisons effect the vampire as well, they will cause them to be in pain, but they heal from it, as vampires are already dead. There are also some poisons which can kill a vampire, and are especially designed to do so. These probably are mystical poisons, or poisons made with holy water, or other vampire weakness.