But that only has "...e å, å i åa ä e ö" -- not the bit about "å i öa ä e å" from that tongue-twisters page, which seems to be a later addition. Ungrammatical, too: I'm sure even värmlänningar would say "på öa", not "i öa".
(Oh, and "e" is of course a contraction of the indeterminate article "en", a/an.)
Further:
e: dialectal version of "det", i.e. "it"
öa, åa: adding an a on the end of a noun is a dialectal way of expressing "the 'ö'" and "the 'å'", respectively.
mentioned in the other comment is understandable to a swedish speaker, but it's written half-phonetically. The words i, å, and ö are properly spelled, however.
“Ö in å” which means island on a river. (Im sure im butchering it, but I’m not to far away)
Maybe you can make this look insane :)