I often visit yahoo answer community and try to help people in Internet related problems. Some day ago, i was browsing omegle related questions.I noticed, most of the users faced omegle ban and Captcha problems.
Omegle use CAPTCHA to keep safe website from spammers, so you need not to worry about it. Omegle captcha is an algorithm to make video chat safe and interesting.
2. Also, change your ip address from modem setting and try omegle.
3. First Clear your browser cookies and cache. Then disconnect your internet connection and connect it again.
Hope, these methods will solve your issue regarding captcha. Otherwise, try other random video chat sites.