All the berries you mention in the last paragraph are also native to Europe.
But the variety you eat today is most likely the "garden strawberry", which is a hybrid variety developed in France by crossing Fragaria virginiana (from North America) and Fragaria chiloensis (from South America).
Other varieties of strawberry are not as popular.
Europeans did a great job further developing crops from the Americas. Italians alone bred tomatoes for every culinary purpose you can imagine.