You can use them at the same time by using different Blend modes and opacity levels.
Good thing to remember is that they stack up in order kinda like if you had layers:
Color Overlay - ( Above Gradient Overlay. )
Gradient Overlay ( Above Pattern Overlay. )
Pattern Overlay ( Below both. )
..and no, you cant change the order. What you can do is use different blend modes and opacity levels as mentioned and you will pretty much be able to do the same thing no matter what order they would be in.
Also, in the layers panel if you open up the Effects ( or FX ) and right click one of them and select Create Layers, you can then control the position of those former layer styles, difference being that you cant control them like you could from blending options because they are layers. You can however put Layer styles in them if you want to.
Duplicate your layer as many times as necessary, one for each overlay effect you'd like to use. For example, if you'd like a color overlay with a pattern overlay on top of that, your bottom layer would be normal with only the color overlay. Duplicate the layer, turn off color overlay on this new layer and select pattern overlay. Then just turn the "Fill" slider in the layers panel (below the opacity slider) all the way down to 0%. This will leave all the blending effects visible while making the actual layer content invisible. This is similar to the "Create Layers" option in the first post, but as with anything in Photoshop, there are always many ways to do things.