I came across a weird bug in After Effects. I applied a stroke (layer styles) to a composition. That composition contains some shape layers and Illustrator layers.
The problem ist the following:
The stroke is correctly applied to the composition, but it generates some weird looking strokes on one of the Illustrator layers inside aswell (check the screenshot). The wrong strokes appear to be on paths inside of an Illustrator layer.

That behaviour seems pretty strange to me.

After long time of trying to solve this, I figured out a workaround:
Apply a stroke with layer styles to the layer in the composition, which causes the problem.
That makes the stroke on the composition correct.