How would you say The other night? Would it be Am oidhche eile?
If you're meaning "one night recently" without being specific, as in "I was out for a walk the other night when I bumped into Iain", you could also say An oidhche roimhe. For "the other day", an latha roimhe
Almost. :) An oidhche eile, the article is am only before labials: m, b, p, and f. ;-)