The feat Beast Strike allows you to add claw or slam damage to your unarmed strikes. since your strength mod is added to claw or slam damage as well as to unarmed strike does it get added twice?
No one knows
It was written in a Dragon magazine, definitely never saw anything like errata, and is ambiguous on this point. Basically, it’s anyone’s guess what they meant. I feel like they probably would have explicitly mentioned something like doubling Strength if they intended that to happen, but there’s no real way for me to back that up.
Personally, I could go either way on balance; kind of depends on how the feat was being used. On a Shifter Monk (the case the feat was written for)? Absolutely, go for it, you’re a Shifter Monk, you need all the help you can get.
On an eldritch claws Warlock sporting levels in Fist of the Forest, Enlightened Fist, and Shou Disciple, Powerful Build and a size increase, Superior Unarmed Strike, Improved Natural Attack, and Snap Kick? Probably would not be nearly so willing.
In short, ask your DM; a good DM should probably answer your question with another: what are you planning to do with it?
Would you say that the damage of a longsword is 1d8 or 1d8+str? I'd say "claw or slam damage" is the damage die you can find in the description of those attacks, choosen according to your size and modified according to feats that change the dice size (Improved Natural Weapon comes to my mind).
While I have no RAW to support my answer, I think this was the RAI.