They all originated in the Anduin Vales

Though I have never read the "M-E book of the origin of plants".
The other things that occured to me were that they are favoured to be eaten by Gollum (but that would not concern the Éotheod, and who knows if Gollum ate strawberries), or eaten by Gríma (but again, you say that it's Éotheod, not Rohirrim, and I am not aware of that he'd eat Rohirs anyway, and who knows if he liked strawberries, too).
Besides that, I have no idea