This is a contraction of “que à l’oral” which in French sounds awkward because of the following e and à. It means orally only.

The word que has indeed several meanings.

In this context, “que” is an adverb in sense of limitation or restriction. The word seulement could be used in that case too. Then, you must have noticed the presence of ne before, in the same clause.

If “que” has been replaced by “qu’” in this particular context, it’s because the “e” elides before a vowel.

For instance, these sentences are equivalent:

Je ne suis interrogé qu’ à l’oral.
Je suis interrogé seulement à l’oral.
Je suis interrogé uniquement à l’oral.