Nick Sugar was born to play the raucous, all-stops-out part of Hedwig in Hedwig and the Angry Inch. In this Avenue Theater production, he got to strut, cross-dress, belt out numbers both sexy and forlorn, boast, whine, mock and beg — and all while he held the audience spellbound. And then he went further, reaching deep into his own soul to find a redemptive dignity amid the squalor.