What can I do to avoid brush strokes in my Mod Podge?
When applying the Mod Podge, use a soft, wide brush and as few brush strokes as possible, as it begins to set quickly. If you can brush it on with only one or two strokes, that is best. Use very thin coats.

Ideally, use a different medium. I think part of the problem is just the Mod Podge itself. I no longer use it because I think it has a haze when it dries. I like to use Delta Ceramcoat Varnish or Annie Howes Glamour Seal. The Glamour Seal can also be used as an adhesive.