They are only meaningless because nobody has defined their meaning thoroughly enough. For me and my colleagues they are definitely not meaningless. We have very clear understanding among us what 'punchy' means. For us it means "big transients", that the part of a sound that contains the 'punch' (the "thud!" of kick or snare, not to be confused with the initial "tick!").
So how to do more 'punchy'? Depends on the sound source of course. Usually on single tracks it is a combination of an EQ and compressor. EQ to boost whatever area contains the energy and a compressor to separate the main transient part from the sustain, thus enhancing the punch.
Warm? Well that one is a bit trickier but when talking to some of my friends and clients the definition has usually been "slightly bass heavy, scooped low-mids and mellow mids and highs.. with some sheen in the very top end".
This can be achieved in multiple ways but it usually means that one needs to tame harsh high frequency sounds like esses, spitty hihats and such (the Maselec MDS-2 being an excellent unit for this task!). Then one needs to keep the overall feeling of the track 'round' and relaxed (kind of a very gentle punch setting, meaning deep threshold, very small ratios, large attack, relatively short release.. so that the compressor 'breathes' with the music, relaxing it a bit). Then do the EQ magic that makes the track "warm".
'Clear' is pretty self explanatory to me.. just make it so that the instruments that have the most important melodies, rhythm parts and harmonies get separation enough from the rest of the mix (this can sometimes be completely impossible if the mix is squashed and all over the place).
YMMV but these are the definitions I've come to use with some of my clients and colleagues. They didn't come simply by themselves.. no, we actually discussed them and agreed on some middle ground so that we could avoid talking about fluffy-silly-things that have no real meaning. Isn't that how language works in general? A word pops up and we slowly get a true definition for it (or sometimes the opposite.. a word pops up and it's precise meaning is slowly but surely diluted).
Having said all that, without meaning, the words do indeed frustrate me. So I agree with you that if a client simply says the words and assumes we have the same translation for each word, then yeah.. it's damn irritating. You'll just have to ask these clients to be more specific.