I currently have rings that need to be at 70% opacity while on the Overlay mode, but it has to be in a group with layer styles applied to that group, as the rings overlap a little. If I apply the opacity and the overlay mode to the individual layers, then there are smaller rings where the overlaps are found. I want to place text underneath one or two of the rings, without adding changing the opacity or the mode of the text. Is there a way that I can put the text in the same group as the rings, but exclude the group layer styles for that one only?
Effects applied to a layer group are applied to the entire contents of that group. There's no way to exclude specific layers from the effects without simply removing them from the group altogether. However, if I understand your goal correctly, it may be possible to achieve the desired effect through masks, while leaving your text layer above the group in the layer stack. Ctrl+click the ring layers you wish to appear "in front" of the text to create a marquee selection of the desired ring layers' active pixels. With that selection active, select the text layer and click the "Add layer mask" button at the bottom of the layer pallet. That should hide from view the portions of the text layer that you wish to appear tucked behind certain rings.
Note: You can adjust the levels of the layer mask if you wish to adjust the transparency of the area where the rings and text overlap. This will not affect how the layers interact with one another. Also, you may wish to unlink the text layer from its mask (click the chain link between them) so you can re-position your text without moving the mask.
*Depending on how your ring layers are set up, you may need to invert (Ctrl+i) the text layer' mask in order to achieve the correct effect.