Bothersome But Normal
OK, the good news first - this is totally normal. I've seen this in my kids and I've seen this in other people's kids. Lots. If this is the only indication of possible ADD/ADHD then I don't think you have anything to worry about (particularly as the doctor says they're ok).
You're In Control
So the first thing is to realise that you - with your partner, if you have one, and anyone else involved in their upbringing, have total control over your children's lives (within the bounds of law and ethics).
Although it's good for them to have their choices and preferences listened to, they don't get to impose their decisions on you. In this case their decision seems to be not to do as they're told until you've told them multiple times at high volume.
This approach:

should not usually be necessary. (Although if you're saving them from alien hunters in the Central American jungle then all bets are off).
Make a Plan
So what you need is a plan. Make this plan in discussion with your partner or anyone else majorly involved in day-to-day childcare (e.g. grandparents, nannies). You all need to be on the same page for this one.
So, working together, come up with some rewards for them doing what their told, and some consequences for them ignoring you.
The consequences should be things that you can actually follow through on, i.e. you're actually going to need to do them, at least once and maybe 4 or 5 times.
So make it things that aren't too serious - e.g. no TV or computer games for the rest of the day. That way it's practical for you to actually go through with it.
It's worth thinking of these things in advance rather than trying to do them 'on the fly', so you can make sure they're proportionate and sensible, and that the other people involved in childcare will actually help you to go through with them (e.g. if you say "no TV today" and then they get TV at Grannie's house later in the day, that's not going to work).
For rewards, I'd go for some small-but-immediate ones - e.g. my kids like pressing the button on the car key that remotely unlocks the car and makes the wing mirrors unfold - and some big ones that they can gradually work up to over time.
Switch Off The TV
When you want to give them an instruction, it's not worth trying to compete with the TV. You can switch it right off, or if you have a DVR then you can pause it (this is what I do), or you can mute it (not as good because the image is still distracting).
This may cause some wailing-and-gnashing-of-teeth type noises from your kids, but I think it's worth it to get over the message "when Dad has something important to say, that's more important than the TV".
They Need To Listen
So:
- you need to get them to stop talking, sit still and look at you,
- you need to get your own face at the same height as their face,
- and you need to get and hold eye-contact with them.
If they're sitting on the sofa then the easiest way to do this is to sit down next to them - if they're sitting on the floor then sit on the floor next to them.
For some reason, most children seem to find it easier to listen attentively when they're sitting down.
Be Concise, Be Clear, Be Decisive
So you've got their attention. Then you need to speak to them very briefly and directly, using language that's appropriate for their age.
Good:
Get your shoes and coats on guys, we're going swimming!
Bad:
I think we might go on a trip, do you want to switch off the TV now or shall we watch for a bit longer? Mum thinks this but I think that. Blah, blah, blah, blah, blah, kids no longer listening at this point.
So I'm not saying don't ever ask their opinion (you should), I'm saying that it's only fair to them that if what you're really doing is giving them an instruction that you want them to follow, that should sound different from normal conversation. Because it helps them to understand that, on this particular occasion, they're being told what to do. Get their opinions at a different time, in normal conversation.
How Many Times Do You Want To Repeat Yourself?
So this is totally up to you. It's not something the kids get to decide. For me, I'm willing to say the same thing three times. The first time I'm just saying it, the second time I'm clarifying/reminding, and the third time I'm giving them a warning that they're approaching what I'd consider to be naughty behaviour:
Firmly: Elsa, put your ice skates on. This is the third time I'm telling you - if I have to tell you for a fourth time then (negative consequence will happen).
So you don't need to get loud or angry doing this - just make sure you have their full, undivided attention. You're explaining to them a choice that you want them to make: do they do the thing you want them to do without being asked/told any more times, or does the consequence occur? It's up to them.
You need to be totally consistent about actually following through with these consequences. If you say that x will happen, then x really definitely needs to actually happen, without fail, every single time.
The first time you do this, they will probably not believe that you actually have the power to make things happen in a different way to how they usually happen - you may hear cries of "but we always have TV". After a couple of iterations - 1 to 5 in the worst-case scenario, in my experience - they'll realise that you actually do have the power to impose consequences on them.
Tones Of Voice
You need to give them some clues as to how you're feeling which don't depend on volume.
Practise using different tones of voice, from 'enthusiastic request' through 'Mary Poppins giving an instruction' to 'I am astonished and severely disappointed that you're even considering not doing what I've told you'.
Rewards
Pretty straightforward, this.
Small rewards: Everyone who gets their ice-skates on without having to be asked more than one time gets .... (small reward).
Large rewards: When I think you've listened really well, I'll put a sticker on your sticker chart and when you both get to 20 stickers we'll go to the theme park!
Counting to 3
Sometimes it can be helpful to find a way to stipulate that you want the thing doing within a reasonable time. I'd wait until the third time of asking to do this, and then go with something like:
Arna, if you haven't cleared up the icicles in your bedroom by the time I count 3 then (bad thing will happen).
1 (normal voice)
2! (stern warning voice)
3. (disappointment that they haven't done it and that the bad consequence will therefore have to occur).
Do give them a reasonable amount of time to actually do the thing - bearing in mind that any physical activity (coats, shoes, etc) is way harder for a little one than it is for a grown-up. Otherwise it's not fair and they'll be able to see that, so it won't create the improvement in future behaviour that you're looking for.
But They Really Can't Hear Me!
If they have no physical hearing problem (maybe check for this?) and no behavioural/psychological/neurological issues then they can hear you. They're just choosing to ignore you (sorry).
The 'Corpse Rule'
When you're telling them what to do - or even when you're just getting their attention, it works best if you give them instructions for things that are active rather than passive.
So the rule-of-thumb is that if a corpse can do it, it's something passive.
Less effective: Be quiet, guys. Stop talking.
More effective: Sit on your bottoms and cross your legs. Fold your arms and zip your mouths shut (make imaginary zipper gesture to own mouth). Now put on your listening ears!
Turnabout Is Fair Play
If you want them to listen to you, then you need to make sure that you make some time to listen to them. It's only fair. The more you can work on improving your communication with them, the better this whole thing will work.
Having 10 minutes at bedtime for you to cuddle them (each of them individually with siblings out-of-the-way if at all possible) and talk about whatever they want to talk about - no distractions, no TV, no anything except cuddle and chat - works really well.
Suggested Reading
Other Thoughts
Expect them to push the boundaries sometimes, that's normal too.
I've tried to present a range of possible tools here - you don't need to try and use all of them at once. Take what works for you. If you only do one thing then make it "TV off".
Hope that's helpful!