Nematodes. Milky spore.

Only some beetle grubs are damaging to grass, and for them grass roots are their preferred food. I've not had trouble with grubs in my vegetables even though I have converted a few grassy, grubby areas to garden over the years. If I come across any (usually at the edges now) I just toss them into the field, used to save them in a jar and out them on the sidewalk for the mockingbirds at my old house.

Turn the soil in the box every few days to help the birds get them. hand pick them.
They are usually only bad the first year, they will disapear as you build soil fertility.

Depending on the grubs you have they can be devastating to your root crops.

In the past we have had a slight grub problem and they liked to eat into our potatoes making them impossible to store.

If you contact Natural Insect Control (they're in Stevensville, ON)

http://www.natural-insect-control.com

they will help identify your pest and provide advice on how to help with your problem.

Good Luck!