Why does Iago want Desdemona, Cassio, and Roderigo to be killed?

Iago wants Desdemona dead because getting rid of her will help him to destroy her husband, Othello. Desdemona is a threat to Iago because she doesn't trust him. So, long as she's around, she can act as what Iago regards as a dangerous influence on her husband, and Iago can't stomach such a prospect. So he sets about convincing Othello that Desdemona's been cheating on him, poisoning the man's jealous mind with lies, innuendos, and snide insinuations. Othello comes to be obsessed with Desdemona's alleged infidelity, and Iago's only too happy to fan the flames of his unhinged jealousy by helpfully uncovering "evidence" such as the handkerchief.
Iago has put it in into Othello's head that Michael Cassio is Desdemona's lover. Again, this is a total lie, but like the most effective lies, it has an air of plausibility about it. After all, Desdemona did intercede with her husband on Cassio's behalf in the wake of Cassio's public disgrace. She's only doing it out of kindness, of course, the kindness of an old and faithful friend—but that's not how Othello sees it. As far as he's concerned, Cassio is making a cuckold out of him and must forfeit his life as punishment.
For his part, Iago hates Cassio for being promoted over him. As a seasoned military veteran, he deeply resents the entitled young aristocrat from getting what he believes is rightfully his. So what better way to get Cassio out of the way than to goad an insanely jealous Othello into killing him?
The hapless Roderigo is a rich, handsome, but criminally stupid, young man. He also happens to be head over heels in love with Desdemona. Iago cynically plays upon his all-consuming lovesickness and tries to convince him that, with his help, he can win over Desdemona. But Roderigo is just the latest in a long line of gullible fools easily manipulated by the evil Iago to do his bidding. When Roderigo finally uncovers the truth about Iago's deception, Iago wastes no time in finishing him off, completing the job started by Cassio in his brief skirmish with the young rake. Roderigo knows too much, and if news of Iago's base treachery and deceit should ever get out, then Iago will be finished. So he murders Roderigo to keep him quiet, for dead men tell no tales.