Pop, it does sound like most of ds's behaviour stems from tiredness (we all get cranky when we are tired after all!) His hyperactivity (and defiance) is probably because he is overtired. And don't worry, he's not turning into the child from hell, he's just acting his age!!!
First, have a rest time in the afternoon, even if it's just quiet music (relaxation or lullaby cd's are great and the babies will like it too!) and a few books. He might not think he needs it, but he does and so do you! Lay down together on his bed or loll on the couch. Make the room a bit darker too. He may nod off, he may not, but at least he is relaxing plus he has the bonus of your full attention which he will love of course!
Next, how is the toilet training going? If it's not going well, maybe it's not a good time to do it? I know you probably don't want to have him in nappies as well as the twins, but you can't hurry these things and if he's not ready (as well as going through a defiant phase!), you are just setting yourself up for trauma on a daily basis! (Been there done that with dd, now going thru it a second time with my ds, hopefully a little wiser this time round!) Of course, this may be irrelevant if he is doing well...!
So far as being impatient goes, don't be too hard on yourself. If ds is pushing your buttons all day you are bound to be feeling stressed out. Take a few deep breaths, try to remain calm and in control. You are "the boss", you can't let him walk over you just because you are too tired or stressed, or he will keep trying you out to see what he needs to do to get a reaction from you. I think Flo2's idea of time-out is good (though sorry I don't like the name "naughty" as it implies they are "bad" rather than what they have done is IYKWIM - we have a Quiet Chair instead, at dd's school they have a Thinking Corner!) We use the microwave timer as it has a nice loud beep, a minute for every year they are (3 minutes for ds, 5 for dd). If they get up out of the chair, the timer is re-started. We haven't had to use it for a while, and when we started they seemed to spend quite a few minutes in there every day, but once they realised it was the real deal, they stopped testing it out.
Choices are a good way to go, as well as good old bribery, if you do X now, we will do Y later. Giving two choices works really well though, since it gives them some say in what happens next. Eg you come and have your bath now or you sit in the chair for 2 minutes - what do you choose? Plus the usual - praise good behaviour like crazy, ignore tantrums and whining as much as possible (!), BE CONSISTENT (eg don't let them get away with something today that they got time-out for yesterday!), distraction tactics, and positive phrasing (eg "walk on the path please", rather than "don't walk on the road please." The last one really works...someone explained it to me once like this - if I say to you, "Don't think of a purple elephant" what is the first image that pops in your head? Right, a purple elephant! So when you say "Don't walk on the road", they are left thinking about the road, not the path! Rather than saying what you DON'T want them to do, say what you DO want instead!
Sorry to go on, HTH though! Be strong you can do it! And just remember, this too will pass!