I have to agree with Lope here. The short tp answer is "Don't do that." But, if you do (and you -- or someone -- will) then note:
mi wile e soweli en kala anu waso. ("I want [beef and fish] or chicken"?) Here you have a mixture (sausage meat maybe?) of meat and either fish or fowl. I suspect what you were shooting for was 'mi wile e soweli e kala anu waso' "I want meat and either fish or fowl" which is, in tp, unambiguous.
mi wile e soweli e kala anu waso. ("I want beef and [fish or chicken]"?) So, you have that here, which means the first one needs another look at. So, it could be that the choice is between a mixture of meat and something else (either fish or fowl) or meat and fish together and fowl. And I see no way to sort those out in this sentence (though a comma would surely help.
mi wile e soweli anu kala e waso. ("I want [beef or fish] and chicken"?). This is unambiguous: You want fowl and then either meat or fish.
mi wile e soweli anu kala en waso. ("I want beef or [fish and chicken]"?) And this is ((meat or fish) and bird) together or (meat or (fish and bird) together).
soweli en kala anu waso ("[beef and fish] or chicken" or "beef and [fish or chicken]"?) (meat and fish)together or bird/ (meat and (fish or bird))together.
soweli anu kala en waso ("beef or [fish and chicken]" or "[beef or fish] and chicken"?) Yup!
As I say, commas would help but basically this should be dealt with at the sentential level and, probably, mixed terms shouldn't get involved in this sort of construction. This is style, of course, not grammar, but intelligibility counts for a lot.
As for grammar, 'anu' is allowed between sentences (as 'en' is not) and also between predicates and direct objects (and everywhere else, in fact, but exactly ow it works in those places (sentences, predicates, DOs) has not been worked out exactly. Does it take a 'li' with predicates say or an 'e' with DOs or a 'la', say. with sentences? Clearly and 'e' with DOs would help here, perhaps more than commas, even. But that won't help in NPs standing alone.