Is there a layman's way of telling when someone can see into your room?

Essentially, you can't look into a dark room form the bright outdoors (or vice versa) because the reflected light from the window is more intense and "drowns out" the light from the dark room. So people might be able to see your lights, but the rest of the room can be too dim to discern.

The strength really depends on the details. The effect can be enhanced by making the window more reflective, i.e. having "silvery" windows. That slightly diminishes the light going in, but strongly increases the reflection. It also depends on the lighting: Direct sunlight shining onto the window and reflecting towards the passers-by is more blinding than diffuse light.

Thus, it's not just a matter of indoor brightness vs. outdoor brightness. You should probably get an intuition by checking yourself (go out, check whether you can see your paintings or furniture or whatnot).

In the end, the simplest test is probably to dance around naked and watch people's reactions.

The glass in a window isn't 100% see through, there is always going to be a tiny bit of reflection. When the light level on both sides are about the same, you see say, an image 90% as bright of the other side, and an image 10% as bright of the inside reflected back to you. But, say the light on your side is much brighter than outside (light on inside, nighttime outside). Lets say the light level outside is only 10% of the inside, then you would see the 10% of light reflected, and 9% of the outside light passing through. You would see more of your reflection than the outside. On the other hand, someone outside would see 90% of the light coming out, and only 1% of the light level as a reflection.

If the difference was any larger, you would barely see them at all, since the inside and therefore your reflection is so bright. Similarly, when you have a light on inside the car, its harder to see out the front window.

If the light in one side of the window is much brighter than the other, it will be hard for the bright side to see the dark side, but perfectly fine for the dark side to see the bright side. A similar (but more pronounced effect) is used for "one-way" mirrors like in interrogation rooms.