It's inconsistent. He *seems* to have super-strength, sometimes, but when the Avengers lock them in a room in the mansion in the original series, he comments that he only appears to have super-strength, and asks why Eli can't bust the door down instead, IIRC.
But I prefer that he does have some super-strength, which, if it's indeed from Mar-Vell, could be solar-powered, and therefore not as useful when he's locked in a room at night, as when he's out during the day (or in outer space, exposed to the light of a hundred stars). Some degree of toughness and flight would also be logical outgrowths from a Mar-Vell powerset. (The energy blasts were most definitely from the nega-bands, and the cosmic awareness from a separate thing entirely, so it would make even less sense for him to inherit anything along those lines.)
And that's me fanwanking again, coming up for a reason why he might claim not to have super-strength in one specific situation.
In any case, his super-strength doesn't seem to be near Hulk/Thing/Thor levels, and IMO, fits better around Tigra (5 ton) or perhaps Spider-Man (10 ton) levels, tops.