When I posted this moth on BugGuide, two people responded with suggestions that it might be an Acorn Moth (Blastobasis glandulella) or another species in the same genus. While this is not quite an exact match for Acorn Moth, the pattern looks very similar and we do have plenty of its larval food source. One other moth from the same night looks very similar and might be the same species.
I am still not sure what this moth is. My best guess is that it belongs among Gelechoidea, but its pattern is very cryptic. It looks very similar to a moth I food indoors in January.
This moth is also still unidentified. It looks very similar to a moth I found indoors a few weeks ago. These little moths can be very tough, so I usually wait until after identifying the larger ones to work on them.
Update: I think that the last moth is a Household Casebearer (Phereoeca uterella).