I don't think you can disambiguate them grammatically other than by rewording them to avoid the ambiguity in the first place.
In practice, they're often disambiguated by context and common sense. "fish and chips" is known to be a single dish, and it wouldn't make much sense for a burger, which can be a meal in itself, to be an alternative to chips, which is just a side. But in the second example, it makes much more sense to have a choice between different types of toast to go along with the salad, than for one type of toast to be an alternative to salad+toast.
However, I've occasionally seen menus that I found confusing. It might say:
Entrees served with a choice of soup or salad and one side dish.
I assume this means "(soup or salad) and one side order", but it's not as obvious as your examples. And all they have to do is reorder it to:
Entrees served with one side dish and choice of soup or salad.
to avoid the problem. I think they write it the first way because they think of the choices in the order that they'll be served, rather than worrying about semantics.