As it happens, none of the examples you've given in your question are of actual English origin:
umbrella is Latin via Italian, and
use,
utensil,
study and
student are Latin via French. Other words like
up and
under are from Old English, while
ugly comes from Old Norse. Here, you can already see some patterns, that the words of Latin origin tend to have one sound (
use,
utensil,
student), while the words of Old English / Germanic origin tend to another (
up,
under,
ugly), but even that isn't consistent (
study,
umbrella). Roughly speaking, these correspond to
IPA /u/ and /ʌ/ respectively.
Other examples: great big clusters of vowels tend to point towards a French origin, like
oeuvre and
bouquet. Clusters of mostly silent consonants tend to point towards very old words of a Germanic origin (
brought,
knight), where one or more consonants have been
elided over centuries of usage.