Of course, you can sue. But the question should be, can you win? So far, you have not provided any evidence that you can.
I will assume you are not in a union nor work for a government agency, which probably means you are an "at-will" employee. If so, both you and the employer have the right to end the employment relationship any time you or they want to for any reason, as long as it is not for an unlawful reason.
You have stated two things that hint at an unlawful reason. One is that you are over 40. It is unlawful to discriminate against an employee who is over 40. But I will also assume you were over 40 when the company hired you 8 months ago. You will need to produce evidence of discriminatory intent, based on your age, if you are going to have any success with a lawsuit.
The other thing you mentioned is being told you are unfit for the org culture. Of course, this could mean you are too old for the young culture you work in. But it also could mean any number of other things and you can be sure the person who told you this, if admitted, will say they meant something work or performance related.
Lawsuits are won on evidence not beliefs. If you have evidence, or believe you have the means to obtain the evidence to support an unlawful reason for your firing, you should have your case reviewed by experienced employment law counsel for a legal assessment. If a lawyer agrees that your case has merit, then you can sue.
One final note: if you do intend to sue for unlawful discrimination, you must first file a complaint with either the California Department of Fair Employment and Housing at http://www.dfeh.ca.gov/ or the U.S. Equal Employment Opportunity Commission at http://www.eeoc.gov/ . Either of these agencies can conduct an investigation if they feel you have the basis for a claim. They also have the ability to issue a right to sue letter but do not ask for one of those unless you have an attorney on board to take your case. Time may be of the essence because you must file a complaint with the DFEH within one year, or with the EEOC within 300 days of the effective date of the termination.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
I assume you contend you are a victim of age discrimination. Such cases are very difficult to prove. Some types of proof would include any "ageism" statements made generally or specifically from management. Whether there was a pattern of laying off older workers in favor of youger workers. Whether in your case a younger worker replaced you, Whether there are financial motives for the employer to favor younger workers over older ones (e.g. insurance, pension costs), etc. In your case, you were hired only eight months ago. That is very powerful evidence for the employer that it did not discriminate against you. Otherwise, the employer can generally terminate you for any reason. You may want to explain the details of your claims to an employment discrimination lawyer to see if he/she has a different opinon. Your time to make such claims are very short. Best wishes.
The harsh reality is employees and job applicants have very few employment rights, and employers have a lot of leeway in how they choose to run their businesses. In general, an employer can be unfair, obnoxious or bad at management. And an employer can make decisions based on faulty or inaccurate information. An employer has no obligation to warn an employee that he or she is not performing as the employer wants. It’s not a level playing field. An employer hires employees to provide work for its benefit, not for the benefit of the employees. Don't expect the employer to take care of its employees; it doesn’t have to and it rarely does.
There are some limitations on what an employer can do, mostly in the areas of public policy (such as discrimination law or whistle blowing), contract law, union-employer labor relations, and constitutional due process for government employees. Please see my guide to at-will employment in California which should help you understand employment rights: http://www.avvo.com/legal-guides/ugc/an-overview-of-at-will-employment-all-states. After you take a look at the guide, you may be able to identify actions or behavior that fits one of the categories that allows for legal action. If so, an experienced plaintiffs employment attorney may be helpful.
Employment rights come from the state and federal legislatures. One of the best things people can do to improve their employment rights is vote for candidates with a good record on pro-employee, anti-corporate legislation. Another way to protect employment rights is to form or affiliate with a union, or participate in a union already in place.
I hope you can resolve your situation and wish you the best.
*** All legal actions have time limits, called statutes of limitation. If you miss the deadline for filing your claim, you will lose the opportunity to pursue your case. Please consult with an experienced employment attorney as soon as possible to better preserve your rights. *** Marilynn Mika Spencer provides information on Avvo as a service to the public, primarily when general information may be of assistance. Avvo is not an appropriate forum for an in-depth response or a detailed analysis. These comments are for information only and should not be considered legal advice. Legal advice must pertain to specific, detailed facts. No attorney-client relationship is created based on this information exchange. *** Marilynn Mika Spencer is licensed to practice law before all state and federal courts in California, and can appear before administrative agencies throughout the country. She is eligible to represent clients in other states on a pro hac vice basis. ***