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I'd imagine that the neighbourhood is helping look after him, since this seems to be a very close-knit community and all. Motorville doesn't seem too too huge, but the place Oliver lives could just be a borough as well I suppose.
Miss Layla and Starey Mary (whose name escapes me.. Myrtle?) would be two contenders I'd think, as well as Ollie's mom's friends. I'm also going to wager that Oliver has not a little bit of magical aid in that regard, though that's never explained to my knowledge.
Hmm.. as for him vanishing for long periods of time, I'd assume he puts in some off-camera time at Motorville when you pop into the Cat's Cradle etc., eh?