I am aware that I cannot expect absolute, definitive answers but there appears to be some common patterns. Are the following reasonably reliable and what can be added?
Clarification: I am primarily interested in classical music here. I am aware that these terms may have very different uses in other genres e.g. jazz.
When I say X is Y, I will mean that it is a reasonable expectation and not a certainty.
A piano sonata is work for a piano alone.
An X sonata (X is not piano) is a duet for X and piano.
Clarification: I am aware that sonata may indicate more than just the instrumentation but it is only the instrumentation that I am asking about here. In other words, what is the most likely instrumentation of an X sonata?
Update: I was thinking of a fairly restricted period. In early music, there is rather more variation in the usage of sonata. Of course, literally it is just something played as opposed to a cantata (something sung). Also of possible relevance is whether X is monophonic or polyphonic. If X is polyphonic then it is likely than an X sonata is for solo X.
A string quartet is a work for two violins, viola, and cello.
An X quartet where X is a specific instrument drops one of the strings and adds an X. I know some exceptions e.g. a clarinet quartet which is actually for four clarinets (one bass).
Update: for some X, a single X plus strings is less likely. You may need to consider whether X is commonly combined with strings.
String quintet adds a fifth string instrument to a string quartet. Most often another viola or cello but occasionally a double bass or a third violin.
X quintet where X is a specific instrument is a work for that instrument and a string quartet.
Update: a similar comment to that in X quartet applies.
Wind quintet - I don't see much pattern here. Wholly or mostly wind instruments probably not all brass or it might be called a brass quintet.
Trout quintet is a work for a trout and a string quartet (or maybe not, exceptions occur).
A string trio is a work for three strings probably violin, viola, and cello.
A piano trio is a work for piano, violin, and cello.
An X trio is less clear maybe X, piano, and cello.
An interesting case is Beethoven opus 11 which can be a piano trio (piano, violin, and cello) or a clarinet trio (piano, clarinet, and cello).
I would hesitate to guess what an X duo was. Maybe similar to sonata.
Sextet and beyond
I don't think that these forms are common enough to say a lot about them. A string n-tet is probably a work for n string instruments. Obviously an X n-tet would include an X but I would less confident what other instruments but maybe all strings. Wind n-tet would even more unpredictable than wind quintet.