Winemaker,
Poast Plus is a great herbicide to apply to broadleaf plants such as strawberries. I use it all the time on sunflowers, peanuts, soybeans, etc but you would need to use it before your berries start to produce fruit. It will only kill the narrow leaf weeds though and it is pretty pricy but you can get it online or in your local farm and garden supply house. I generally apply only 12 oz to 25 gallons of water. That mix with a little crop oil, will do an entire acre but the directions will tell you exactly how much to use for strawberries. Hope this helps...