I daven Nusach Ashkenaz but I often daven mincha in minyanim with a different nuasach. Should I say my ashekanzi tachanun or is there a minhag ha'mokom? Moreover I have noticed sefardim davening their own tachanun in my ashekanzi minyan. If I can get Halachic sources that would be great!
Igros Moshe Orach Chaim 3:89 - last paragraph says that if ones Nusach is not to say Vidui & 13 Midos, and is in a Shul that does say Vidui & 13 Midos, he should definitely say the Vidui & 13 Midos. He says one has to follow the Minhag of the Shul he is Davening in, in any situation where it is noticeable.
Rabbi David Lau says that one who Daven's Ashkenaz, and finds himself in a Sefard Minyan should say his Ashkenaz Tachanun, however when the Chazzan says Vayavor you should say the 13 Midos with the congregation.
אתה אומר את הנוסח שלך, אבל כשהחזן מכריז ויעבור, אתה אומר עם הציבור את י``ג מידות
You must daven the tachnun according to the nusach you normally daven. The kitzur shulchan oruch says that one cannot chop and change nuschaos as they are all weighted and each word is counted. If you would like to add vidui before tachnun then that's okay, but you should try not say sephardic tachnun when davening in ashkenaz l'moshol. Rav Moshe Feinstein was very strict on staying with one's nusach.
Rav Moshe Feinstein's rule of thumb is that for quiet portions of the davening, you have your choice of using your nusach or the minyan's. (Though the chazan's own quiet shmoneh esrei should follow what he'll say for the minyan five minutes later.) For parts that are public/out-loud, you should use theirs.
I haven't seen him address tachanun, so I would assume that you have your choice of what to say quietly; however if they're all standing when you're sitting or vice versa (e.g. nusach sefard starts with nefilas apayim on Mondays and Thursdays), I don't know what Rav Moshe would say.