So, I was invited to host a mini piano and orchestra concert at my school despite having a little knowledge of classical music. I have some problems with the naming conventions of some musical pieces, like Beethoven's Piano Sonata No.6 in F Major Op.10 No.2. How exactly do I pronounce "Op.10 No.2"? Does "opus ten number two" sound awkward? And is it okay to just skip that part and just say "Beethoven's Piano Sonata No. 6 in F Major"?
"Opus ten, number two" doesn't sound awkward, but I'd recommend just omitting it. Those numbers are good to have when searching in some sort of catalog, or if someone (like Bach) wrote 100 pieces called Prelude and you need to distinguish between those. So if there would be a prelude from Bach on the list, it makes sense to say "now you will hear Bach's prelude in D minor, BWV xyz". But, in the case of the Beethoven piano sonata, the "Beethoven's Piano Sonata No. 6" fully identifies the piece, so I think you could say just that. Adding the fact that it's in "F major" can help because it may stick in some people's minds better than the number 6.
(And imagine yourself sitting in the audience and hearing someone say that "Beethoven's Piano Sonata No. 6 in F major Op. 10 No. 2" will be played. How long would you remember the "Op. 10 No. 2" part? I personally wouldn't even pay attention to it.)
I would actually drop the number 6 instead and keep the opus. Opus numbers are the composers own numbering, while the ordinal number are more the view of an accountant. Ordinal numbers are also not as stable: Some symphonies of Schubert and Dvorak have two established numbers, and the pecularity of Bruckner with a 0th and even 00th symphony appear also wierd.
Popular names (like moonlight sonata) help the auditory, but are frequently invented by an early publisher. So they may may given as addional hint, but not on their own.