If you're using Python 2.7, you can use a dict comprehension:
unidict = {k.decode('utf8'): v.decode('utf8') for k, v in strdict.items()}
For older versions:
unidict = dict((k.decode('utf8'), v.decode('utf8')) for k, v in strdict.items())
(This assumes your strings are in UTF-8, of course.)