I would suggest the use of a stirrup hoe at least weekly, especially in the walkways.* You can also use any of the mulch materials you mentioned.* Strawberries do best with straw as a mulch, hency the name.
Vinegar is also an organic herbicide.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.