|| and "or" (as well as && and "and") have nothing to do with numeric vs strings. They both are simple tests, the only difference is in their priority: the "words" ("and" and "or") are of a lower priority than the ones a C programmer would know (&& and ||).

'or' is safer to use in some cases because it almost guarantees that everything to the left of it binds tighter (gets evaluated as a single expresion) and *then* gets tested. It's really on a case by case basis. A good and consistent use of parenthesis can often prevent making such decisions, as it removes the the precedence ambiguity.

I think you're probably confusing the difference between or and || with the difference between, say, lt and <. There is no relationship between the two differences.

or and || act the same (they have the same short-circuit behavior), but or has a much lower precedence--meaning that you can use it after list operators without using parantheses. Read perlop for more details.