I read in The Truth that Otto carried around Imp food, and I checked and this was confirmed in Pratchett Wiki (http://wiki.lspace.org/wiki/Imps), but I remember it saying in an another book that Imps were insubstantial beings, "barely more than just coloured air", and also demons. Why do they need to eat, and what could you possibly feed an insubstantial demon?

Presumably they eat something, since they're living beings, but it might not be the same as human food. (Remember those salamander things in TCOM that eat light?) Why they need to eat is, according to that article you linked to, because it keeps them alive longer. Also, for the record, the imps in the iconographs are Brownies, for punning reasons.

Mrs G
The Garner who cares.

The earliest mention I can find about the iconograph imps is from 'Moving Pictures' and although it is clear the imps have to be fed otherwise they get fractious, pTerry doesn't give any idea as to what they eat. I would assume its only smaller portions of whatever is available to the other humans. Something must be happening to the food however as there are several mentions made that the imps also need mucking out at regular intervals.

I suspect that as they are minor characters it is sufficient for the reader to know that they exist in one form or another in iconographs, watches and Dis-Organizers.

I want to die peacefully in my sleep, just like grandpa. Not screaming and panicking like his passengers.
Don't drink and drive from The Lancre Tavern

Surely they're discussed in TCOM? Twoflower's iconograph is an important feature in that book, as I recall. It's even a plot device.

Mrs G
The Garner who cares.

Buzzfloyd is right. This is from TCOM:

And an explanation: