I found the logic of the strength bonus for offhand/twohand strikes a bit lacking in some circumstances.
If a character with a +0 strength mod is wielding a weapon offhanded or using a twohanded, it makes no sense that they still have +0 in both cases.
Don't even get me started if the character has a -1 penalty...
I've created an alternate more sensible table drawing on the rules as the basic principle
(str mod) (offhand) (twohand)
+5 +2 +7
+4 +2 +6
+3 +1 +4
+2 +1 +3
+1 +0 +2
+0 -1 +1
-1 -2 +0
-2 -3 -1
-3 -4 -1
-4 -6 -2
having negative modifiers to a stat, such as strength, represent the inability to effectively use particular weapons. If a player has a -4 mod to his strength he should probably be a caster. if a player has that 2 or 3 strength, chances are she cannot carry any two handed weapons, armor or anything of use at all, as the carrying capacity for a 3 strength is 30 pounds max load. arguing that negative modifiers should have bonuses on damage is the same as giving a 3 year old a 5 pound sledge just to see if they can do anything besides hurt themselves. having half your strength mod with 2 weapon fighting makes some sense, but there is a feat to get rid of that. while having negative stats can add some flavor to a character, as a gm you should draw a line at how low it can/will go. a pc needs to have a 3 int to even understand speech because beasts are generally a 2 or 1. all in all having your own creative ideas is always a good thing.
I just imagine an elven wizard with 10 STR with a Longsword swinging it with two hands should hit harder than swinging it with one.
Likewise if he had a dagger in his offhand he shouldn't be hitting as hard as if it was in his mainhand.
The rules account for this when the player has a strength bonus, but not when they have a penalty or no bonus.
I put the table down to 3 Str for completeness.
My only real complaint is remembering the table. The nice thing about the current system is that it's a simple, branchless function of the normal Strength modifier--floor(1.5 * modifier). This one, it'd take a while to memorize. (I still don't have, e.g., bonus spells memorized.) Until then, we'd have to write the table down to use it, especially when things buff or debuff Strength with any frequency.
Edit: That is, memorize the table, or remember the rule that modifies the center values. Neither is particularly easier than the other for lazy gamers that already have enough numbers to juggle.
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I like that a Str 10 character gets a damage bonus with a 2-H weapon in this system.
I never liked the limitless ability score expansion in 3.0. At what point does a character's Str bonus exceed the material strength of the weapon? Was a Medium longsword really meant to be wielded by someone with a 32 Str?
I've toyed with capping all damage bonuses at the weapons max damage (except maybe fighters). But you still get some large numbers.