You should really ask these kind (I mean, "the Rules" kind) of questions on the "Rules and such" board.
In any case, you don't add the damage of the natural weapon to half strength. Natural weapons do their DV worth of damage.
One very important detail: the 'half strength attacks' do Stun damage, not Physical.
I have to say that I didn't find creatures where their natural weapon is lower than half their strength. Which creature(s) are you talking about? Maybe their natural weapons have reach or armor piercing or something else to make it better?
Edit:
Wait, looked again.
Hunter Seekers have 3 Str and only 1P damage. *shrug* They're early models, maybe a glitch in how they're made? Or just give them 1 more damage, maybe the writer rounded down instead of up by mistake.
The Gorgon has 20Str and 8P NatWeap damage, but it does -2AP and +2 reach. Oh, minor detail: also venomous, paralyzing and petrifying!
Hydra is 30Str and "only" 10P -2AP. But again, stun vs physical damage, not to forget an IMMENSE +4 reach and seven to nine attacks per action!!!
Sea Serpent: armor piercing, venomous and possibly reach.
So, in all but the Hunterseeker's case, I'm sure your players will gladly have those monsters do (Str/2)S damage instead of using their horrible, horrible natural weapons.