Here's the relevant text from the Core Rules:
Unarmed Strike: At 1st level, a monk gains Improved
Unarmed Strike as a bonus feat. A monk’s attacks may be
with fist, elbows, knees, and feet. This means that a monk
may make unarmed strikes with his hands full. There is
no such thing as an off-hand attack for a monk striking
unarmed. A monk may thus apply his full Strength bonus
on damage rolls for all his unarmed strikes.
Now, does the bolded portion meant to clarify simply that no matter what part of the body a monk uses, he or she gets full strength bonus damage?
Or, would a fighter/monk (with the TWF feat) get full strength damage on an unarmed strike that actually was being used as an off-hand attack?
The very next sentence in the text you quoted, right after the bolded portion, answers your question.
Monks always do full STR damage on their all unarmed strikes. This is true even if they multiclass. And it applies to off-hand attacks because, as the bolded part says, there is no such thing for a monk.
Well, that's what I thought, but the wording is pretty much the same as 3.5, and according to the last FAQ, a monk could, in fact, use an unarmed attack as an "off-hand" attack (p19), which seemed a little wonky to me, so I thought I'd ask.
FAQ:
The description of the flurry of blows ability says
there’s no such thing as a monk attacking with an off-hand
weapon during a flurry of blows. What does that mean,
exactly? Can the monk make off-hand attacks in addition to
flurry attacks?Actually, the text to which you refer appears in the entry
for unarmed strikes. When a monk uses her unarmed strike
ability, she does not suffer any penalty for an off-hand attack,
even when she has her hands full and attacks with her knees
and elbows, using the flurry of blows ability to make extra
attacks, or both.
The rules don’t come right out and say that a monk can’t
use an unarmed strike for an off-hand strike (although the exact
wording of the unarmed strike ability suggests otherwise), and
no compelling reason why a monk could not do so exists.
When using an unarmed strike as an off-hand attack, the monk
suffers all the usual attack penalties from two-weapon fighting
(see Table 8–10 in the PH) and the monk adds only half her
Strength bonus (if any) to damage if the off-hand unarmed
strike hits....
Of course, this was before PF changed FoB to include TWF, so I'm unsure of how the monk's IUS interacts with non-flurry TWF, now.