Hmm, I'm not sure what connotation of "awkward" is being used, whether it's "uneasy/nervous" or "unexpected/strange"...(or both!)
But for awkward ("unexpected") romance, mine goes to....
Satsuki and 'The Beast' - "X" - I mean seriously. Love with an android? Okay, easy enough. Love with AI program who looks and acts very human (AI Love You)? Okay, sounds good. Love with a big metal thing the size of a small car shaped kind of like a giant kidney bean?
ALERT, ALERT. But, that's part of what made it unique I guess.
For awkward as in "uneasy"...I'm with stelok about Hibiki and Fuuko from IMMSE. That was just...I dunno. Even I was feeling weird imagining that one, but it was there, and at the end I was actually pretty PO'd. Well, extremely PO'd.
After all that, I was about to yell at the tv screen I was so mad.