I play Swords and Wizardry Complete, where there is no "Exceptional Strength" score. I like the idea of "Bend Bars / Lift Gates" as an ability one has, but suggest that you make it a fighter class feature instead of based specifically on Strength scores.
I use Jack Shear's suggestion that all Thief skills use the Hear Noise d6 table, modified by my own rule that Assassins, bards, dandies and monks (and all other classes that receive thief skills) use the same rule, but at -1 compared to thieves (so whereas a thief starts off at 3 in 6 and goes up, other classes start at 2 in 6 and go up).
I propose that we use an identical table to the Thief Hear Noise d6 table for feats of strength - singular exertions of power and force - that a fighter wishes to perform, whether battering down doors, hurling boulders back at giants, hoisting the portcullis of the castle, dragging the elephant he's just lassoed to its knees, picking up an opponent and using them as a living missile, etc. Barbarians, rangers, paladins, etc. may do the same thing, but at the same -1 penalty that thief-like classes suffer in comparison to thieves using their skills. In cases where it might constitute an attack, an attack roll skill needs to be made, this roll simply allows the feat to even be possible in the first place.
The intent here is not that fighters are automatically the strongest class around (though they do tend to be), but rather than this represents their capacity for heroic exertion under stress. I recommend against allowing it to replace normal athletics tests for running, jumping, swimming, climbing, etc. (I will be using Skills: The Middle Road in Necrocarcerus when I start it up again). Instead, this is precisely there to cover the exceptional feats that we read about in epic literature that are otherwise not well represented in the rules. I encourage players to come up with exciting and interesting feats of strength for use in the game.
There are no limits to how often fighters can use feats of strength, and I encourage a permissive attitude, since this encourages fights to follow unpredictable, dynamic progressions involving the feats of strength. Individual referees may wish to establish beforehand with the players of fighters whether these feats of strength can actually be superhuman (as some examples mentioned above are), or merely at the extreme limits of what is humanly capable (the strength of the exemplary mother lifting a car off of her children in a fit of adrenaline).
One simple possible variation of the rule would be to have the feats of strength be merely humanly possible until a player hits 9th level, and then allow them to become superhuman.