The postal relations between the Imperial government and the States were enormously complex: there were all sorts of permutations of what could be sent where. However, the only stamps from the feudal States permitted for postage
outside India were those of Travancore-Cochin, from the 6 June 1950 until September 1951, when the Travancore-Cochin Post Office was finally folded into the India Post Office.
This is an example of a cover from Travancore-Cochin to Ireland, during the period such use was permitted:

Philatelic of course, but virtually all such covers are.
This cover, from Jind State


made it to the USA unscathed, but the use was strictly illegal. Jind overprinted Indian stamps were valid throughout India, but not abroad.
For the most part, State stamps were only valid within the State that issued them. Mail going outside the State was supposed to carry Imperial stamps as well, to cover the postage beyond the State borders, like this cover from Poonch State into British India:


Some States insisted on the use of State stamps on
incoming mail from British India, like this postcard from Indore City to Jaipur State

And occasionally the States were permitted to set up their own post offices in British Indian territory, when the Imperial post office didn't have any post offices in the State. This cover


was sent from the Las Bela State Post Office in Karachi (now in Pakistan, of course, but then in British India) to a village in Las Bela State, because there were no Imperial post offices in the State.
And I could go on ...