Stop the debate. One parenting philosophy I'm trying to enact in my own home is "Save the words for happy times". Lecturing or arguing with kids more often than not backfires, so instead, use as few words as possible, but be 'action oriented'. Your son won't pick up toys? Say once in a calm voice "Please pick up your toys, or they will have to go in time-out". If he doesn't comply immediately, calmly start putting them in a bag. He may start protesting at this point, but I would ignore it. Then, put the toys away somewhere for a while (maybe a week). When he's calmer, you can talk more the situation. (E.g., the next day he asks for the toys, you can say "I would love to give you your toys honey, but they need to stay in time out until "X" ... I'm sure next time you'll put they toys away yourself".
Interruptions are tricky, because they are self-rewarding (they almost always work to get your attention). When he does it, you can say in a firm voice, "Honey, I'm talking to X, you need to wait." if he interrupts again, use fewer words "Wait your turn". If that doesn't work, maybe escort him to time out.
Simultaneously, I'd practice as much positive reinforcement on problem behaviors as possible. Your son interrupts you two times, but does eventually let you finish the conversation? Turn to him warmly and say "Thank you so much for letting me finish! It can be hard to wait your turn when you have something important to say, but you did it! Excellent job! Now I can give my full attention to you. What did you want to say?" The idea is to 'catch' them doing good things (even taking a small step in the right direction) as often as possible, and giving them lots of attention for it, while simultaneously giving them less attention while misbehaving.
I've also instituted reward charts for two of my three year-old's problem behaviors, and I was amazed by how well they worked. The reward can (and in my opinion should) be tiny ... its more about remembering to take notice of good behaviors. So, every time he puts his toys away without complaint, you praise him and let him pick out a sticker to put on his chart. When his chart is full, you can give him a small treat (an extra TV show, a trip to the ice cream store, small toy, whatever).
None of these is going to fix the problem completely (he's 3 after all!), but hopefully they would help. Two parenting books I really like for dealing with things like this are "Love and Logic" and "How to Talk So That Kids Will Listen ... ".
Good luck!