Three approaches to the refusal thing (in official terms this is called noncompliance).
You can look at the approach in e.g. the ABCs course I mentioned or it's probably the same in 123 Magic, basically any of the modern behaviourism will cover this - which has a guide to how to do time out in the most effective way - they recommend very strongly against getting into that cycle where you are physically taking them to the step as this is counterproductive. They basically say establish a norm where time out is followed by the child and to do this you use a backup sanction e.g. removal of a privilege for a short time, so screen ban or a favourite toy (not a comfort toy) goes away or something, and then don't engage further. You can also just skip the time out part and go straight for any sanction where you don't require the compliance of the child, ie it's totally outside of their control.
They do stress that time out/punishment won't actually achieve anything on its own so in order for this to work you also should be working on praising compliance (ie doing as he is told) hugely any time you see it at all and/or using some kind of reward system e.g. a sticker chart or points system specifically to target compliance. They also have some pointers on how to give instructions to children in ways which are more likely to gain compliance, which is basically stuff like using a lighter tone, being specific, offering a choice/challenge, being playful.
Second option, which overlaps a lot with the positive half of the behaviourism part is to ask in a less demanding/confrontational way e.g. make it fun (throw stuff into a box, get a toy dump truck to carry the toys, put music on and do "dance cleaning"), be playful e.g. have a competition to do it fast/pretend to be cleaning robots/play the floor is lava at the same time, present it as a logical thing e.g. "I really want to do this with you but it's going to take a while to clean this up. Do you want to help me and we'll see if we can get it done quicker?" Or present a choice e.g. we need to clean up, would you like to tidy the trains or the lego? Empathise about how he must be feeling tired and everyone doesn't like tidying up, give wishes in fantasy, do it together, do some other tidying chore while he's supposed to be doing his - loads and loads of great suggestions along these lines in How To Talk.
In addition to this add the "connect before you correct" thing as Dan Siegel/Tina Payne Bryson say. So when he's going no no no no - rather than treating that as noncompliance which must be squashed you treat that as him holding up a little sign saying "Everything is awful and I'm not OK" (which is a bit dramatic, but, y'know, three year olds. Their emotions do feel dramatic to them.) and take a moment to connect with him and see if you can figure out what's up. Quite often if they are in a bad mood they will just automatically "NOPE" at whatever you ask because it's almost like they take that instruction/reminder as an invitation to battle and it's sort of a "you're not the boss of me!!" retort. You can either do this in a silly way e.g. act mock outraged that he said no and (with a little flair/wink/smile so he doesn't think you're being serious!) threaten some dire and terrible fate, or launch into a tickle/dragon/snuggle attack or whatever works for you and you know he will find funny. You can often diffuse the tension this way and then once that has gone, he'll likely be more open to some of the other techniques like the choice or reasoning or a game or whatever. Or if you don't want to do that then try approaching with empathy as though instead of saying "No! I WON'T clean up! You can't make me!" he had burst into tears. So "Hey? What's up? You sound upset, is something wrong?" Listen and see what he says, offer validation of feelings - again, once he's said his piece he'll likely be much more open to sorting the mess whether it's a bit of a nudge from you, or a compromise offer/bargain from him, or whatever it is.
Or third option, which is a bit polar opposite to the first one - don't ask him to do stuff if he's going to refuse, or if you do ask him to do something, don't have a hardline expectation that he will do it specifically because you have asked him - ie, don't even have compliance as an expectation at all. Have the expectation/keep the value in mind (in the case of tidying, the value might be respecting stuff/taking good care of posessions/keeping the house usable by everyone/sharing household responsibilities/maybe a mixture of all these things.) But not compliance.
When you drop compliance as a goal you get less of the random butting heads just for the sake of butting heads - and when you do encounter that then you treat it as a sign that he's a bit out of sorts (basically like the second option, but rather than being "connect before you correct" the aim is literally just connect - trust that the "correction" will work itself out in time. If it happens in that moment naturally, then win win.
In terms of how to get the other expectations met which aren't compliance related - you have so many tools to do this which don't involve trying to force compliance. Modelling, being explicit in what you're doing when you model, ie not waiting until he goes to bed to tidy up, maybe explaining as you go, helping him in his tasks, offering him the option to help you in all different tasks (not only insisting that he does his/you do yours), breaking things down into smaller steps or aspects and working on them one by one, thinking about the skills involved in the thing he's not doing as well with and working on those, all of the positive/playful/empathetic suggestions in the previous approaches, if it's a routine kind of thing, and you're not getting a lot of success with it, look at whether it would fit better somewhere else in the routine (e.g. rather than let's all tidy up at the end of the day, can you go in and help/encourage/model tidying up little and often so it never gets into such a mess), whether you could control the environment to prevent the problem coming up as frequently (e.g. have fewer toys available - declutter, curate and/or rotate). Talking (at neutral times, ie, not as a direct attempt to persuade him) about your goals or expectations e.g. that you're trying to ensure there's always a clear path through the front room or you want to keep his books nice so they don't get broken, so he really gets that reasoning and then when you do want him to put something away you can remind him of the goal you talked about. Modelling (again, because it's probably the most important one, you cannot expect children to do something they never see you do).
Three approaches (I don't think either of them is inherently better or worse than another, they all have pros and cons) - different things work for different families. Just an idea, anyway.