How do you avoid brush strokes in satin finish when painting around casings?
Putting on paint with a roller adds a texture to the paint as you may have noticed. This is controllable to some extent by the choice of roller used. 

Cutting in around windows and ceiling corners almost always wants to be done before doing the roller work. (The professional painters I have seen painting at the place I work always do it that way too). After the cut in painting has dried then you do the roller work and allow the roller to come up as close to the corners as you can without getting too close. This allows the roller texture to cover over the cut in painting. 

Using a pad painter or foam brush as recommended in another answer here has good merit toward reducing the brush marks. However a brush, especially one with a beveled angle edge, gives a lot more control over the painting in corners and along ceilings than you can get with a typical foam brush. I have found that planning for multiple coats of the cut in painting and the putting on each coat in a light manner will greatly reduce brush marks as opposed to getting over exuberant with the paint.