I've never tried to measure strawberries by transferring them to an old quart box, but there really would be no way to be very precise. The problem is that when such things are sold in pints or quarts they still vary, depending on how "heaped" the boxes are, and how big the fruit is. The bigger the berries, the bigger the spaces between them can be. One website I found suggests that a pint of whole strawberries equals 2 1/2 cups of whole berries, 1 3/4 cups sliced. Sounds about right - measure a pint or quart (2 or 4 cups), and heap it.
What sort of recipes are you using? Unless you are making jam or some such thing, it is likely that the exact amount of fruit is not crucial. For a pie or something, just go with what seems right - it's your dish!