I don't know about Lady Gaga, but alot of them seem more Bajoran than anything else. Granted the only show that really had off-duty wear was DS9, but come on Cryptic, we don't need to be going around looking like Vedeks.
I think they went with the Jammies look to appease the "No Bikinis on Sol Station" crowd. So now you don't have swimwear in the space station... but you also don't have it on the beach... and they technically lived up to their promise of off-duty casual wear.
I believe the clothes to be as much Vulcan and Romulan influence than anything. The skirt (Robe bottoms) I believe to be a sadistic joke by Cryptic in response to the outcry for a community wide skirt option. /facepalm