What is the best way to fill in the holes in aluminum siding?
Do you have (or can you acquire) any pieces of aluminium or other non ferrous metal at all?

If so you could cut small squares that will fit over the holes, screw them over the hole using self tapping screws and seal round the edges of the patch. Painting would give it an extra layer of protection.

It might not look particularly pretty, but will do the job until you are able to replace the affected pieces.

Alternatively, some sort of mastic filler might work, but you'd have to check it adhered to aluminium otherwise it would just fall out. However, I think this would look worse than a patch.