Task Master is an excellent anchor against certain teams and not so solid against others. The fact that 2 blocked arrows + 1 blocked super in X-factor 3 kills Phoenix makes me feel he has an incredibly useful XF L3 With Ammaterasu in the center if things are going relatively badly I can have X-factor L3 Task with 3-5 gauges and that just means you need to force people to start blocking since on block it can kill 2 characters very quickly. Arrow punishes are amazing and his normals beat the vast majority of other normals in the cast.
I swap Ammaterasu to anchor occasionally but feel the team works pretty well in any order. Although Viper can be fine with X-factor level 3 I feel she gains the least out of it, her combos already kill so the increased damage is rarely important (Just was at a tourney where I fought F-champ, had I x-factored I would have won since less gauge would be built when killing Phoenix and I’d already taken 2 of the 3 necessary wins against him. >.<) the main thing I feel she gains out of X-factor is slightly increased mix up speed and the ability to chip characters to death very quickly with Seismo, in X-factor it only takes 4-7 Seismos to kill Sentinel as an assist which is incredibly easy, they cannot summon assists against X-factor Viper. Ammy gains vastly superior chipping ability and her combos kill for dramatically less needed gauge. On top of this she has forever to hit confirm into X-factor in brain dead sections of combos. Task’s speed increase and chip increase are the things that I appreciate the most, it makes him have to change a lot of his combos, but the damage output kills off of pretty much any connection, and full screen arrows xx legion arrow does almost 800K.
As for potential third characters that work with the 2 it really depends on your playstyle, though here are a list of a few that I feel gain a lot from either Viper, task, or both:
All around good:
Ammaterasu: Arrows assist her damage, easy Viper OTGs are more damaging and less scaling than sword OTGs, amazing DHCs from and to both characters. Provides cold star for unblockable set ups and scary albeit unnecessary resets. Great normals. Cons, low health.
Dante: Doesn’t require either assist much, but can use them for certain things like teleport shenanigans with Task arrows and unblockable set ups with Burn kick has good DHCs and multiple assists of his own that are very useful for the other 2. With Crystal and Task Arrows Viper easily breaks the Wesker killing damage line, Crystal assists Task fighting characters that have low air mobility like Mags, Viper, Ammy, etc. Jam session sets up unblockables on the way in, etc. Great normals. Cons, low health (I’d say execution as well but you’re playing Viper.)
Rush down good:
Zero: Can take good advantage of Task arrows for mix up into pressure, provides an exceptional full screen DHC, Sougenmu assists are amazing for Viper, good DHCs in combos and outside for safety. Great normals. Cons, low health.
Magneto: Chips like a bizzle with Task and EM disruptor, more rush down skills, good DHCs after Viper, takes advantage of Viper OTG assist or Burn kick assist very well, arrows help his approach and can DHC glitch into Task master. Great normals. Cons, low health.
Great for Viper:
Spencer: Although he has DHCs and can benefit from the other 2’s assists well, slant shot is without a doubt the assist with the scariest purpose for Viper. It allows her to convert 3/4 of the screen away Seismos into a dead character on hit. Solid user of X-factor and gauge that the other 2 can leave him with if worst comes to worst. Wall of health. Cons, Slant shot has very little use for Task.
Broken tier:
Phoenix: People assume that since Viper can burn through meter quickly that she doesn’t work with Phoenix, using TK shot and horizontal aim master assists Viper can easily do 700K or with better execution death combos while building 2 or more meters as can Task Master. Having her on your team forces people to play differently against you. People giving up chances to kill Viper is almost as painful as them giving up chances to kill Phoenix. Gives you the best use of X-factor in the game, gives the team both solid and random potential. Takes great advantage of Taskmaster’s health and gauge from seismo chip.
Cons: Much more necessary thought on meter management, Viper and Task are both great at blowing away meter if they want to, but are also amazing at building it, figuring out when killing a character is or is not worth the meter is very important. You need to be calm and collected if Phoenix gets snapped in, though having her die far from kills the team. Task and Viper are the only assists you should ever be able to summon outside of combos with this team. 
In my opinion this is one of the best teams in the game, but is much less easy to use than others. None of the characters are assist only status and if any of the characters have meter and x-factor hard countering them is near impossible, they all will always kill characters they hit in X-factor mode, so if things go badly you need 3 hits to win the game.