What relieves itching eyes on the outside of the eye, more like the eyelids area?

Try these: I typically recommend moisturizing/lubricating eye drops as a first approach for these symptoms. If this isn't sufficient then next i'd usually suggest an allergy eye drop (anti-histamine). Avoid long-term decongestant drop usage. Also, if you wear it, consider whether you might be reacting to makeup or some other topical facial product you're using. Good luck.