Several attacks get only half the Strength bonus to damage – off-hand attacks or attacks from light weapons come to mind.
Of course, main hand, non-light attacks get the full Strength bonus and two handed attacks get 1-1/2 times the Strength bonus.
When Strength is lower than 10 I'm sure main hand, non-light attacks get the Strength penalty to damage.
What about the other two cases? Do they get the Strength penalty as well or do they get half that? If it's half that, how is half of, let's say, -1 calculated?