Certain adjectives (凄い and 足りない come to mind) seem to be able to take 物 as a prefix, but I haven't been able to find anything on the internet regarding this. Are the forms with 物 more formal or something?
It depends on what adjective it takes. It's difficult to generalize, but you may say this もの make adjectives more "subjective" in some cases.
もの足りない and 足りない both roughly mean "not enough", but they have different meanings. もの足りない only means "not satisfied" psychologically. I don't think there is any difference in formality between もの足りない and 足りない.
For example, you can say お金が500円足りない but cannot say お金が500円もの足りない. これだけの練習では足りない means your practice is objectively not enough to win a race, while これだけの練習ではもの足りない means the practice was too easy and you want to get harder one.
もの凄い and 凄い are almost the same, but もの凄い is more emphatic. They are both relatively colloquial.
As for もの悲しい (vs 悲しい), this もの means "somehow" or something like this. This always refers to one's subjective sorrow/empty feeling without explicit source of sorrowfulness. You can say 悲しい出来事 but usually not もの悲しい出来事. You can say 秋はもの悲しい but saying 秋は悲しい is a bit puzzling to me. There is no difference in formality.
The same goes for もの寂しい, although this is not common.
See: 籾山洋介 「足りない」と「もの足りない」 教養のある日本語 教養のない日本語