Asparagus generally should be grown separately from other food crops. In the case of strawberries, as the berries runner and spread, they'll have the same effect as weeds, competing for moisture and nutrients as they take root near the asparagus plants. Also, when the asparagus plants go to fern, they'll cast shade on the strawberries and reduce their yields. So while it might seem efficient to grow the two in the same space, yields of both will be affected.