What is a food grade, tasteless and odorless "food glue" that would
dry hard and not be too sticky.

Egg yolk.
monroe22

Cornstarch mixed with hot water makes a good glue.

egg yolk could go bad- looking for something with a shelf life. would
the corn starch go bad?

nathank000-ga: No, Dried egg yolk will not go bad. Ever hear of egg
tempera paintings? Been around for 500 years. But, if the egg yolk is
immediately subjected to moisture, it would not be practical. The
question as posted did not spell out the conditions.
monroe22

No, cornstarch is great!  Mix with hot water to make a paste whatever
consistency you like.
Can even be cooked to make it harded.  Sometimes used to hold shut
taquitos before they are deep-fried.  Also, can be used to patch a
hole in a spring roll before its fried.

Lots of fun, also:  Mix cornstarch and cold water, to a consistency
thats like thick liquid, like honey or something.  then pull or pour
it out of the bowl into your hand.  then squeeze it and knead it and
play with it.  Gets HARD like a solid when you squeeze, but when you
stop squeezing, immediately acts like a thick liquid, trying to ooze
out of your hands.  fun for the whole family!