Calm down. Remember that plants have been growing just fine for millions of years before humans came along and tried to help them. It isn't too late to prepare a bed but you might do best to just remove the sod completely rather than trying to kill-it-and-till-it.

If I were preparing a bed for strawberries on short notice I'd remove the layer of sod and about the first 4 or 5 inches of soil below that. I'd fill the shallow trenches formed by the removed material with a mixture of native soil (the dirt from the hole) mixed with organic matter such as compost. After planting the strawberries, making sure not to bury the crowns which is a sure way to cause them to rot, I'd mulch heavily with straw.

A google search will return thousands of results about how to set up for and care for strawberries. The link below is just one of many great online guides to strawberry culture.

Here is a link that might be useful: Strawberry Growing 101