If you directly report to one of them then the answer is simple - do what they're asking and ask them to handle the other two for you (that's part of their job).
If you directly report to someone who isn't one of the three, then go to them and ask for their support in dealing with the situation - use them as a gatekeeper between you and the Problem Three.
If you don't directly report to anyone, or the person you report to is unwilling or ineffective at helping you (this should be the least likely situation, but sadly I suspect it's actually the most likely) then the situation is harder. You say you "don't have the clout to sit them all down", but that's probably what you actually need to do. Arrange a meeting with all of them, with the agenda of setting your priorities (again, do this only if you don't have a clear line manager responsible for setting them already).
Get them talking to each other rather than all talking to you independently, and in the future when they inevitably still tell you to ignore the other two, you'll have the outcome of their meeting together to point to and say "no, I'm doing it like this". It would be a good idea to ask another senior person along as well - maybe their common boss if they have one, and definitely your line manager (the person you directly report to according to the HR paperwork).
Right now they're trying to bypass and undermine each other by bullying/strong-arming you, as they perceive you as a weak link that they can use to get extra priority for their project. You need to try and remove that avenue from them.
I had a similar situation once as a junior employee. I was assigned to two projects - one that needed me in the main office doing small quick tasks, and one that needed me sitting in a client's office half an hour away doing essentially nothing. The project manager of the first one would get frustrated when not enough tasks were being done, and the project manager of the second would get frustrated whenever he saw me in the main office, as it meant they couldn't bill the client for me sitting in a chair. Annoyingly, the same person was the project manager for both projects.
I should have arranged a meeting with him and my line manager to discuss my projects, the priority of each, and their expectations for how I would manage my time. What I did instead was get increasingly frustrated until I quit due to stress, and had to take 4 weeks off before the start of my next job. I wouldn't recommend going that route.