I don't see 'eatable aboard' as incomprehensible or meaningless. It might refer to food items on sale at an airport terminal, for instance.
I'd say that 'productive selection' is hard to find a meaning for but contexts are imaginable : 'George was given the job of deciding what lines of goods we could sell in our shop. He made a very productive selection - these lines will sell'.
'Hysterical soft' : or 'hysterically soft' ? Either phrase might be used to describe a person who was so so supine that their condition was hysterically funny. (Not a charitable description.)
A 'square circle' is in any usual sense of the words logically impossible : nothing can be at the same time and in the same respects both a square and a circle. But that might be the point of using the phrase : 'According to your schedule you're supposed to be in London on Tuesday at 09.00 hrs and in Tokyo at the same time. That's impossible, like drawing a square circle'.
There is a different but related phrase, 'to square the circle'. When someone is trying to do what's just impossible, you could say that they are trying to square the circle. The point of that phrase is that it is geometrically impossible to create a square equal in area to a given circle. (But then, with alternative geometries I wouldn't put money on it.) I think it's true in Euclidean geometry.
Perhaps we move in different circles, Euclidean or otherwise, but I can't say I've ever heard your four phrases used. But I take your word for it.