E., I had to laugh when I read your post as it brought back such good memories of when my daughter did this same thing. We called her our little Lady Godiva because she not only would strip the minute she came home, she would run outside and swing on the swingset in the back yard! More than once I ended up chasing her around the house, her in her birthday suit, out the back door and in the front! :) After awhile I would just shut the back door and hold open the front door as she came around. I'm sure the neighbors thought we were odd, but she was happier once I relaxed about the whole thing and now I remember it with a fond shake of my head.
First off, I kept a big towel handy to wrap her in when she would run outside. Second, I let her do as she felt when we didn't have company. I totally understand your frustration! My daughter finally outgrew this around age 7 though her outside journies ended at around age 5. Still, she would change her clothes frequently until she was about age 10. What is behind all of this? DSI, Dysfuncation of Sensory Integration. There is tons of stuff on it on the internet. Basically, her nervous system is maturing at a slower rate. There are things you can do to help her nervous system mature such as brushing her body with a special brush, once she is diagnosed with DSI (sometimes called SID), a PT can show you how to do this and more. Talk to your pediatrician about it and if they don't believe in it, try another pediatrician until you find one that will test her for it. (some doctors still do not believe in it but I have seen amazing results happen with treatment)
I did all these things with my daughter and it did help, but really, time is what it took for her to outgrow it. My daughter is now 13 and I'm happy to say, does not change her clothes more than once a day (when she gets home from school she changes to something more comfy for her) and the Lady Godiva bit has totally gone away much to my relief! She can now communicate to me when certain materials bother her and her wardrobe is more suited to her sensitivity needs and she can do her own laundry. When we started treatment for her, her need to strip diminished to a controllable level and I would spend extra time with her treatments before/during company so that she would remain dressed while they were visiting. (we often had people stay for the weekend). At the same time, I let go of worrying about it and when it was just the family at home, I would allow her to do as she needed with her clothes, only asking that she wear a towel or wrap in a blanket if she was outside of her room.
Like I said, getting her treatment for DSI helped immensly and we were able, with treatment, to bring her need to run naked to a managable level and gave her the tools she needed to communicate to us her sensory needs. Good luck! And remember, this too shall fade into a pleasant memory :)