When my son was at university, he knew of an establishment catering for the gastronomic needs of the student body which promoted itself with the appealing slogan:
MORE NOSH FOR YER DOSH
The OED’s earliest citation for nosh is, with a variant spelling, from ‘The Times’ in 1873:
Evans’s music and supper rooms…Jolly Nash every night at half-past 11.
It appears to be cognate with modern German naschen, ‘to nibble, eat on the sly, to eat dainty food or delicacies’. My son didn’t comment on the nature of the comestibles provided, but my guess is that they didn’t exactly match that last part of the definition.
As for dosh, ‘Chambers Slang Dictionary’ relates it to doss, that is, ‘a place to sleep, a bed, a lodging’. The OED’s earliest citation for that is from 1789 and betrays its probable origin in dorsum, the Latin for ‘back’, on which a sleeper might be supposed to lie. The variant doss came to be used as the money paid for a place to sleep, and Chambers dates this use to the mid-nineteenth century in the United States, after which it ‘then vanished, to re-emerge in the UK in the 1950s’ as a general slang term for money. Dosh now seems to be more popular in British English than in American English. The British National Corpus has 18 times as many records of it as the Corpus of Contemporary American English. The balance between the two for ‘nosh’ is more even.
All this is a rather long way of saying that there seems to be something about one-syllable words ending in -osh which places them slightly below the line of verbal respectability. Others are cosh, gosh, josh, posh, slosh, splosh and tosh. I’ve no idea why this should be.