This response (scroll down to the second Q&A) to a question about whether a gardener who uses his Christmas tree branches as mulch on his strawberries should be concerned about pesticide residues appeared just before Christmas in the New York Times:
Oh, well then. Carry on.
A: Probably, but probably not enough for serious concern, especially if you remove the boughs in spring before the needles drop.
The use of pesticides on Christmas trees is decreasing, and most are applied in the growing season. This does not magically render them benign, but it does mean that they largely migrate or degrade before the tree is marketed. Any ill effects fall primarily on the farm, its workers and its environs, not on your strawberries.