Have you done a Google search how to renovate a strawberry patch?  Without looking, I think recommendations to mow the tops off, fertilizer, .......   

However, bindweed & vines.... I think it is going to be difficult if not impossible to clear these up with chemicals.  Hand-pulling and/or spot spraying with glyphosate might be your best chance, and spot spraying is going to risk getting glyphosate on your berry plants and kill them.  

How large is your patch?