In Tolkien's conception, humans and Elves are anatomically identical.
I suppose that actually the chief difficulties I have involved myself in are scientific and biological - which worry me just as much as the theological and metaphysical (though you do not seem to mind them so much). Elves and Men are evidently in biological terms one race, or they could not breed and produce fertile offspring - even as a rare event: there are 2 cases only in my legends of such unions, and they are merged in the descendants of Earendil.
There might be some criticisms of Tolkien's biology there, but I think we can safely say based on that statement, the answer to your question as it regards Elves is that yes, they have a pancreas, just like people.
Dwarves are trickier. There is no similar statement as far as I know. We only know that Aule created them while having the Children of Illuvatar in mind, but he was a little unclear what they actually looked like. Nevertheless, since he did make them as misshapen replicas of Elves and Men, and they have the same diet, I think the answer here is probably also "yes", other than some skeletal differences they are probably pretty much the same.