Privacy claims are gauged on "expectations of privacy," and while in public, there's very little expectation of that. People who see you are free to comment about your actions and/or appearance, and free to photograph you and comment about the photo. Websites are just an extension of that freedom.
However, there's a form of privacy right known as "false light" that protects you from being portrayed technically truthfully but in way that implies a falsehold, such as filming you when stumbling and insinuating that you're drunk, when you're actually wearing high heels or walking on an unsteady surface.
Depending on what kind of website this is and why this was offensive, it's possible that you have a claim, since there's also a form of privacy that protects you from disclosure of embarrassing facts, but the 1st Amendment is very broad in the types of commentary it covers, and while it refers to government speech, if this was a comment-worthy photo on matter of public interest (also a broad category), then the speakers' speech is likely to be protected.
There are also publicity rights in CA that protect you from having your image exploited for profit, such as uin advertising or endorsing a product.
You need to realize that these kinds of claims can be expensive to mount, and can force you to identify yourself (right now it appears that you're anonymous) and to call more attention to the photo and comments that you wish had never existed. You may be best off ignoring it.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Most likely not. If the picture was taken of you in a public place, it is not likely to be an invasion of privacy. If the picture is being used to sell a product, it could be a violation of you right of appearance, but it does not sound like that is the case. Consult an attorney if you are interested in taking action, though your choices may be limited.
Wow. Even our politically correct, grotesquely sensitive, sue-over-anything society does not permit a person file a lawsuit simply because they "feel offended" by public comments that are made about them.
We used to be a society of adults, enlightened by experience, mature in our dealings with others, and hardened by life. It was that society that established courts to adjudicate those intractable disputes which proved unresolvable by reasonable men. It is most certainly NOT the role of our courts to provide a forum, or to placate, those who feel offended simply because they've been embarrassed in public.
If the person who took your picture in a public place thinks that your "actions and/or appearance" is "weird" and "odd-looking" then he has a right to shout that opinion from the rooftops -- or to publish it on the web.