You should consult with an employment attorney, who will evaluate your case and if you have a good case, make a demand on your behalf.
Under California law, unless you have an employment contract or were terminated for an unlawful reason (such as discrimination or a violation against public policy), an employer can terminate your employment "at will" with no reason and without advance warning, and does not have any obligation to pay severance pay. For these reasons, you really need an attorney to advocate for you. Otherwise, you can only collect unemployment benefits (no severance and no lawsuit).
Contact an employment law specialist first. The circumstances surrounding your termination may give you bargaining power if you decide to seek severance pay. Contact your state and local attorney bar associations and get referrals from them for an attorney who specializes in wrongful termination. Good luck!
Your question asks whether you should "ask" for severance or sue. This implies the employer has not already offered it. The real choice for you, therefore, is not whether to sue or seek severance, but whether (a) to sue and then seek severance, or (b) do nothing at all. In reality, a lawsuit will often apply pressure to the employer and create an opportunity for a settlement short of trial. Of course you can always hire an attorney to ask for severance, but you often need to be willing to file a lawsuit if you want to get the employer's attention. This obviously assumes that you have valid grounds for which to file a lawsuit. To answer that question, you should follow your instinct and call an employment law attorney. Many will offer free initial consultations to discuss the facts and determine whether you have a case worth pursuing.
As a related matter, you should probably seek unemployment benefits. There is really no downside to doing so, as long as you are always honest and forthcoming with the Employment Development Department ("EDD"). If you are denied your unemployment benefits, contact an employment law attorney who has represented clients before the California Unemployment Insurance Appeals Board ("CUIAB") before. That person will greatly increase your chances of success on an unemployment appeal.