The confusing thing about sound card and synthesis terminology is terms often get conflated when describing different things.

In traditional analog synthesis, an oscillator is a basic wave form generator. Typically this would be a sine wave, triangle wave or square wave. This signal would get run through additional circuitry (e.g. filters, amps, gates) which would further shape the signal into its final sound output.

In the case of the GUS, it is using digital PCM samples for audio generation. That is what an "oscillator" is in this context. The reference to 32 "oscillators" simply means it can play and mix up to 32 mono PCM samples simultaneously (or 16 stereo PCM samples).

I don't know the actual implementation of the GF1, but I did some software synthesis when I was in college. Basically, when you have a wavetable or sample based music system, for every channel you keep track of the position of where you are in the sample. Each output cycle you update your position with an addition that is proportionate to the pitch of your voice. If your sample position exceeds the pre-defined loop boundary, you wrap it around. You then use your sample position to look up the data to be used, using some interpolation to account for the fractional portion of the current position.
The GUS has no notion of "multiple samples per voice" because it is just doing a bunch of math and keeping track of a bunch of variables. In a lot of synthesizers, more than one sample is used to create a layered sound or just to save space. For example, if you sample the sharp attack of a piano (the hammer) and the sustained sound of the string, you can optimise the latter sample with a small loop instead of using a lot of memory to store the complete sound of the piano note. But this costs (temporarily) an extra hardware channel. The GUS doesn't do any such thing, but it was designed so that the middleware or end user software would take care of such things.