To me, the answer is no, at least not a functional or practical one. There exist some Pokemon with the versatility to take up any of those roles -- Pokemon like Mew and Arceus come to mind -- however, mixing all three into one set is a bad idea. Here are some of the flaws with the idea off the top of my head:
- Four moveslots would not give a Pokemon the capacity to support, wall and sweep for a team.
- Three roles would require EV investment in more stats than is logical or effective.
- If you depend on one Pokemon to do too many things, you may be significantly disadvantaged if it goes down in battle.
- Most Pokemon simply don't have the moves or stats to do all three at once effectively, limiting the amount of teambuilding options you'd have and the amount of ways you could incorporate a Pokemon like this into a team.
Due to these (and other) potential limitations, one Pokemon would do a mediocre job at best of any one of those individual roles, if they're combined with two others. Why not split the roles across multiple Pokemon that actually do a good job of them? You could say that it saves a teamslot, but when the Pokemon saving the teamslot is mediocre and is now a team member you depend on a lot, I don't really think it's a worthy trade.
Even the concept of doing two dedicated roles at once like you brought up is a bit precarious, at least the way you've presented it. Pokemon that immediately come to mind as tanks like Conkeldurr or Metagross can wall or sweep to some extent, but in my opinion, don't fit the exact requirements for either. They are bulky and can absorb some hits, but they don't wall Pokemon the way that perhaps Ferrothorn would. Similarly, they can deal some solid damage, but I don't think they're going to be your win condition sweeper like Pokemon such as Greninja or Blaziken could be. They incorporate elements of both sweeping and walling, but don't completely do either, if that makes any sense. They don't sweep or wall; they tank.
Any Pokemon that attempts to do three roles at once is subject to these same concepts; they incorporate some elements of those three roles, but can't do all with nearly the same effectiveness that would be achieved by two or three different Pokemon. To explain what I mean, I'll take this Clefable as an example (credit to Smogon). Clefable is one of the most versatile Pokemon in the game right now, and is the Pokemon I think best fits your description.
Clefable @ Leftovers
Ability: Magic Guard
EVs: 252 HP / 172 Def / 84 SpD
- Calm Mind
- Thunder Wave / Flamethrower
This Clefable mixes elements of sweeping, walling and supporting into one set. It offers Calm Mind and Moonblast to set up, deal damage and potentially sweep through a couple of Pokemon before going down. It packs sufficient bulk to take hits for the team, and has a good defensive typing in pure Fairy. It packs the ability Magic Guard, which allows it to absorb status like burn or poison freely, and also packs Thunder Wave and Soft-Boiled to support its team and increase its longevity. Though this Clefable incorporate elements of three different roles, I would not depend on it to do all of them for my team. This is why I don't think it is truly a tri-role Pokemon, and is an example of why I think no such thing exists in a useful and practical form.
This Clefable can tank hits for sure, but can it absorb that incoming +1 Mega Charizard X Flare Blitz the same way my dedicated wall Pokemon could? No, so it's not really a full-blown wall. It packs a great set-up move in Calm Mind and has a strong STAB attack in Moonblast, but is it an immediate offensive threat like my sweeper Pokemon is? No, so it's not exactly a sweeper either. It packs a great ability and some great moves for team support, but in this context, is it as helpful and annoying as a support Pokemon like Klefki? No, so I wouldn't play it as a support Pokemon like Klefki. Does that makes sense?
My response to your query regarding a sweeper + support Pokemon is largely the same; I don't think there's a perfect two-in-one Pokemon like this. There are Pokemon that can incorporate elements of both -- say a sweeper like Excadrill which also runs Rapid Spin, a support move, as filler -- but those Pokemon don't contribute to my team the way a Klefki, Chansey, Liepard etc. would as a support Pokemon.
I guess the validity of this answer, and the validity of any response to this question, depends on how you define a Pokemon that does three roles in one. Feel free to disagree with my logic, but my personal opinion is that a Pokemon only fits three roles if it can do each individual one with similar success to a Pokemon that does it as their only role. I don't think a Pokemon like this exists; however, if you define it as a Pokemon that merely incorporates elements of three roles (but isn't the Pokemon you depend on for all of them), then I've just given you a Clefable set that fits this criteria nicely.
Sorry if this was hard to understand!