Mysterious ん.

Recently I read somewhere that in some words some vowel + consonant + vowel combinations that now aren't always spelled with an ん used to be, and that in those cases although the kana has vanished it still affects pronunciation. I knew about あまり amari (あんまり anmari), and that it's sometimes a thing, particularly with female singers, to add that sound (as in Misora Hibari's "晴れる日(ん)が来るから" (hareru hi [n] ga kuru kara) and Miyuki Nakajima's "いつか、話せるひ(ん)が来るわ" (itsuka, hanaseru hi [n] ga kuru wa")—both very specific structures, but all that's occurring to me right now—and now in an e-mail from 先生 I see すんごく (vs すごく). What's going on here phonetically? When and how did this come about? Will have to look into it and find some more examples. There must be a known pattern.