IFR use of handheld GPS

I've seen other discussions get off topic and go on about handheld GPS
use under IFR. And people get all worked up about it. I know there is
a lot of history on this newsgroup, but I haven't followed most of it
(so don't lynch me, please).

It seems that a lot of pilots believe a handheld GPS shouldn't be used
while IFR. And a lot more believe that it can't be the "primary"
navigation method. Sometimes that makes sense, but other times it
doesn't (to me). So here are a few questions I have that work up to
GPS:

1) Can you use celestial navigation while IFR? And does your sextant
have to be "approved" in some way?

2) Can you use dead reckoning for IFR navigation? If so, can you use
your wrist watch as your "primary" timer? Or does it have to be an
"installed" clock? And to do dead reckoning calculations, can you use
a drugstore-bought calculator? An abacus? Or how about a handy "dead
reckoning computer" that calculates ground speed and track?

I can understand that a handheld GPS is not supposed to be used as a
substitute for VOR or DME or ADF (say for navigating along airways or
for shooting instrument approaches). But can you not use one for
flying off-airway routes without playing tricks (like pretending to
double-check position with VOR/DME or asking ATC for a vector and then
ignoring the heading they issue)?