First, you should be aware that a California LLC can do business in Delaware just as well as a Delaware one can, so you may not actually have a reason to "move" the LLC. If you decide that you want to exchange your California LLC for a Delaware one, you will probably need to get a new EIN. There might be ways to avoid doing so, but they would probably be somewhat complicated.

Second, if you convert the LLC to a corporation (whether S or normal) you will normally have formed a new entity for tax purposes and the new entity will need a new EIN. Again, there might be ways to avoid that result, but they would likely be complicated.