Taller will eventually equal dominant, via shading out of the little guys underneath. Excepting where there's some type of allelopathy, the secretion into soil by one plant species of compounds which inhibit other plant species, this fact should come to predominate the site. Quackgrass is another story, precisely because it does have allelopathic effect5s on the plants around it. I'd concentrate on that one and not be too concerned with the strawberries.

+oM