Hi Tracey, vine weevils do love strawberries! There's no guarantee the grubs won't eat the immature roots of your veg, but it might deter them (I've never heard of vine weevils eating carrots, parsnips and leeks). It's a good idea to lay a thick layer of gravel over the soil surface to prevent the adult beetle laying eggs in the compost, but I wouldn't recommend this when soing seed! Alternatively, you could use nematodes (http://bit.ly/HkZ1BA) to safely kill the vine weevil grubs. Apply this to your trough twice a year and you'll still be able to grow strawberries.
Hope this helps
Kate