If some trans* people themselves prefer "transgendered," that's fine. But as a general rule, trans, trans* or transgender are preferred to "transgendered." This is primarily because "transgendered" has medicalized connotations, like it's a condition--a nasty association considering our (continuing) history with the Standards of Care.
Tr***y is a slur used overwhelmingly against trans women, and many non-binary male assigned at birth (MAAB) trans* people. It connotes "man-ness," and transmisogyny, and it's really only okay for trans women and some non-binary MAAB people to reclaim it.