any

It can be any but there's another word for university student: hallgató. (literally: listener)

Storytime! :)

The -o- is regular, -a- is the exception. So for new loanwords, it's always -o- (unless it's -e-, of course.)

The words that take -a- used to end with an -a, but we lost those worthless sounds. Finnish Estonian for example didn't, so you can still see those -a's at the end of the appropriate cognates.

Examples: - ház (hun: house) kota (fin: hut) (yes, these two are actually cognates.) - hal (hun: fish) kala (fin) - máj (hun: liver) maksa (fin) - száz (hun: hundred) sata (fin)

The ones above all take -a-

EDIT: also, conjugated words might take -a- regardless of everything I said above, but there are rules for those. So for instance the accustaive of piros (red) isn't pirosat because of some etymological wizardry, but because it's derived from the (now unused) word "pir."

One more thing:

dia = slide strip (filmstrip),

diák = student OR slide strips (plural),

diákat = slide strips (accusative, plural),

diákot = student (accusative),

diákokat = students (accusative, plural)

Okay, actually it was five more things.

From what I heard, -t and -k endings after back vowels can get -o- and -a- in different words, and there aren't any easy and clear-cut rules when to use when. I think at this point it's better to just memorise.

It's very short, but it's there.

There are not hard-and-fast rules, but a few clues you can follow.
For diák, for instance, remember that 'i' and 'í' are kind of wild-card vowels. They can appear in either front- or back-vowel words and have no influence on the harmony. For words that only consist of i or í it's often a bit of a guessing game: hír, liszt, szín (news, flour, colour) get front-vowel treatment, híd, ír, íj (bridge, to write, bow) have back-vowel harmony. In earlier days of the language there was another i-like sound, one that was spoken a bit more gutturally, which since merged with the front-i and left us with a bit awkward vowel harmony rules. (My favourite by the way is 'biciklizik' - to ride a bike. I still don't know exactly which harmony it uses, but I think it's a front-vowel verb.)
In other words you have stray 'é' in otherwise back-vowel words, like béka (frog) or acél (steel). Those have back-vowel harmony. Same issue here: there was a different sound earlier on that got merged with the é.
Now, with the rare true mixed words (which are mostly foreign words), you generally take only the last vowel into account. Like technika - technics, which is treated as a back-vowel word.

It's a rather narrow case, but there sure is a context where I'd say this.

"This is a university city. It is full of students."
"Where do you see a student? There are only old folks here."

Perhaps, "This is the faculty club. Where do you see a student?"

It's not a robot voice. :´)

It's definitely an 'e' spoken here. An 'a' sounds much darker. The 'gy' sound of egy is not well pronounced because of the 'd' that's following.