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.
In other instances of adding entire attack's worth of damage, via such things as Scorpion's Grasp or Imp. Trip + Knockdown, et al, the Str bonus is added twice. In the ones that don't (Palm Throw, others), this is specifically called out. Unfortunately, there's very little/almost nothing else that directly adds the damage from one attack to another, without requiring another attack/attack roll, and it's all obscure. There are instances where Str bonus to damage is replaced (Targeteer Fighter, Control Body) and spells or abilities that add natural attacks seem to assume that the added Str is part of your 'claw damage' or whatever.
Interestingly, the only direct comparison I can think of is Manyshot, which conflates multiple arrow attacks into a single attack roll with multiple sets of damage. The only thing it mentions in terms of str or damage (composite bows, hank's power bow, that elven bow that adjusts to str), is that you calculate DR and damage separately for each arrow. Which would seem to indicate that the status quo (bow damage + str if composite + any other modifiers (weapon specialization etc) for determining damage remains.
But really, like always, it depends on your party optimization. If they are t3+ and know how to swing it, then your t5/4 ass needs the help. If they're rolling single classed fighters and healbot clerics, just add the die from the slam.