I think the insects feeding your strawberry plants are cutworms. Cutworms feeds on leaves, stem and fruits. There are different type of cutworms (like variegated cutworm, black cutworm and rough skinned cutworm) which feeds on wide varieties of plants including weeds. The adult moth lay eggs on leaves or stem. The newly hatched larvae starts feeding on crown leaves by forming webless perforations. The older larvae cuts the stem and also feeds on leaves by making irregular holes.
Cutworms are nocturnal insects, so they feeds in the night and hide at the plant base during day time. Generally the cutworm larvae curl into a C-shape when disturbed.

Management:
1. Keep a close eye on plants regularly. If you find any egg mass on leaves or stem remove and destroy them.
2. Hand pick the larva (better during night) and put them in soap water.
3. Spray homemade insecticide soap solution to repel/kill the insects (add 1 tablespoon of cooking oil+ 2 tablespoons of baking soda+ few drops of Ivory soap in 1 quart of water).
4. Also you can spray biocontrol agents like Bacillus thuringiensis, or spinosad.