Malware is an all encompassing any rogue software on your computer: a worm, virus, trojan horse, adware, spyware...anything.
Virus is a piece of software that spreads from computer to computer. Usually they email itself as an attachment (GIF, Jpeg, video, greeting card, document or whatever), to everyone on your contact list

. It may or may not be malicious (usually they are).
Adware is
unwanted advertisement and is usually packaged with other software. Damn annoying ads too boot, since they're take up monitor real estate and are usually a pain in the (_!_) to remove. Once they hit the realm of a pop up you cannot close, that's when you question the parentage of the adware author and wish bad things upon him and his kins for 4 generations.