"more than three"

[Tuonelan Joutsen]

I know that it's possible to say things like Enemmän kuin kolme opiskelijaa tuli juhlaan. But I also know that there are several other words that mean something like "many", and that they have comparatives. Can you say things like "more than three students came to the party" using, say, useampi? If so, does it change the meaning, or are there situations where it would be correct to use one but not the other?

[jahasjahas]

I'd say Juhliin tuli yli kolme opiskelijaa.

Let's break that down:

1) The order of information seems more natural when you start with "juhliin".
2) If you talk about "juhla" on its own, you'll most likely want to use the plural. (But compare: joulujuhlaan tuli..., kevätjuhlaan tuli..., syntymäpäiväjuhlille tuli...)
3) "yli" seems to fit best here; I'd use "enemmän" or "useampi" when I'm actually comparing two amounts of something. (I'm sure someone can come up with a better rule on their usage.)

[Pursuivant]

You could say Juhliin tuli useampi opiskelija. Which is more than just a few. Juhliin tuli muutama opiskelija, means at lest the 3, but could be 99 students, fewer than useampi anyways. Juhliin tuli pari opiskelijaa / Juhliin tuli pari-kolme opiskelijaa is a couple of students, not necessarily 2 or 3. Juhliin tuli muutama hassu opiskelija. so you could pack up and call it a day.

Juhliin tuli useita opiskelijoita, then again means there was a crowd of other people but quite a few students showed up. Juhliin tuli usea opiskelija then again means, that of the college most of the students showed up.

Useita vaihtoehtoja

You can use monta approximately in a similar manner. Its more common used reporting no-shows though Juhliin ei tullut montaa opiskelijaa.

[Tuonelan Joutsen]

Oh, it's interesting that you can use yli like that -- in general it seems roughly equivalent to "over" in English, but "over three students came to the party" feels to me like a somewhat odd sentence. (Seems like English "over" needs a large number -- or maybe just a large quantity, independent of the numeral: "I waited for the bus for over three hours", which is perfectly natural, vs. "I waited for the bus for over three minutes", which sounds odd to my ear unless you're in a world where the buses come every thirty seconds or something).

And I'd failed to take into account the fact that in a sentence like this, the party would be more likely to be old information than the number of people who came. So does Juhliin tuli enemmän kuin kolme opiskelijaa sound better? How about Juhliin tuli enemmän ihmisiä kuin vain minä?

[Pursuivant]

Well if someone was going ballistic over waiting the bus 'yli kolme minuuttia' it would be silly in Finland as well

[Tuonelan Joutsen]

Yeah, I was just surprised because I can't think of a situation where it would make much sense to say "over three people" in English -- "more than three people" is always going to sound better, I think.

[Pursuivant]

Well yo don't "smoke" in Finnish either, you "burn".

DO NOT BURN HERE! TOBACCONIZING PROHIBITED!
(Älä polta täällä! Tupakointi kielletty!)

Make sense of those in English

so no use trying to find logic in figures of speech, just ain't there