In English, we can put the word 'only' almost anywhere in the sentence and mean different things. And, yes, you are right that in some places in can be ambiguous such as the example you provided, but that example shouldn't be ambiguous. Americans have gotten lazy.
1) Only he eats pasta on Sundays. (Not his sister.)
2) He only eats pasta on Sundays. (He doesn't buy it, play with it, make it,...)
3) He eats only pasta on Sunday. (He eats nothing else on Sunday.)
4) He eats pasta only on Sunday. (Not on any other day of the week. -or- similar to #3, just pasta on Sunday.)
5) He eats pasta on only Sunday. (needs more, "... on only one Sunday of the year.")
6) He eats pasta on Sunday only. (Not on any other day of the week.)