What uses for what movesets

Ice Beam is far from garbage. While it's no Avalanche it's usually tied with Blizzard for performance on any ice type that can learn both. Ice Beam makes Mewtwo the strongest ice type attacker currently in the game. Mamoswine is likely to oust it, assuming Niantic doesn't conspire against the brown woolly.

Thunderbolt puts Mewtwo as the 3rd best electric attacker behind Raikou and TS Zapdos. While that makes it currently better than all non-legend electric attackers that could change with Gen 4's release.

Flamethrower is the Hyper Beam of the new moves. It's better than other fire types in a generalist sense but when weather and specialist factors play in it takes a back seat to the usual suspects.

I'd like to stick an Ice Beam one on my ice type roster for variety's sake. Hitting hard while lacking the typical ice type weaknesses is pretty dope.

At the moment, Mewtwo with Ice Beam looks to be the best overall Ice attacker in the game. Jynx still has better DPS, and others beat it in TDO, but it ranks very highly in both categories. However, there isn't much call for it at the moment and there are a few Gen 4 mons that are likely to surpass it.

With Thunderbolt, it's very good but Raikou and Zapdos are better. With Flamethrower, it fall quite behind the pack but it's still fairly reasonable.

My gut feeling, not backed up by any numbers, is that Mewtwo is now the Swiss Army Knife Pokemon. Can do many jobs well, but few of them optimally.

C/P is still best Psychic attacker, and there will be uses for that down the line. I'll be replacing the one I TM'd to Shadow Ball last week.

Focus Blast is the same - pretty good, but Machamp can do the job too, and without using Rare Candy. Unpleasant to fight against, best countermove against Ttar.

PC/IB isn't terrible - in fact, it's probably best Ice attack right now, despite lack of STAB and lack of an ice quick move. That's only because most Ice attackers aren't that good at attacking. Mamoswine should be better, but if they give it crap moves (or no ice charged move, which would be really mean) it might not live up to it's potential.

Thunderbolt isn't a bad move, and Mewtwo with it will probably be not as good as Zapdos or Raikou. Not sure if it outperforms Jolteon or not, but it should be in that ballpark.

Flamethrower is all right, and my gut again puts it in the same ballpark as Flareon, weaker than Moltres or Entei, and almost certainly well behind Heatran. IMO this is the least useful of the moves.

Since you mentioned Kyogre, if it comes back yet again, TB Mewtwo should be one of the best counters to the Blizzard set in case you don't have enough high level Raikous/Groudons. Being able to tank one Blizzard makes a huge difference and C/SB Mewtwo was already one of the best B Kyogre counters just dealing neutral damage. Tiny niche, but it is there.

Like everyone has said already, IB is by far the most useful out of the new moves, I'll probably try to power up one if I can collect enough candy for it.