When I was 18, I was arrested for burglary (felony). The State Attorney ended up dropping the charge to trespassing, and I was able to get a waiver and a clearance. How were your charges dismissed/sealed? The way I did this was to do Pre-Trial diversion, and as it turns out, the Navy considers that an automatic admission of guilt. Also, when you were told you don't have to inform your employers about offenses in your sealed record, I don't think that includes the military. Sealed or not, when they do a background check on you for a security clearance, it will come up, and you'll be questioned about it. Be honest about it from the beginning. To warn you, you will have to sit and have a one-on-one interview with someone of intimidating importance at your local MEPS to explain what happened and to prove that you've moved on.
As far as whether or not you will be able to get a waiver, that's really not a question anyone can answer. It all depends on the demand for nukes at the time. Since I joined the Navy, the economy has (sadly) gotten worse, and consequently, retention has gone way up. So the Navy may not be as desperate as they were when I was joining. The link sovbob posted is probably helpful; however, chances are, any limiting regulations pertaining to what is or is not waiverable, can probably be waived itself. There's a waiver for just about anything when applying for the Navy - even a waiver for having too many waivers.
In short, the best way to answer your question is to try. No matter how bad the economy is, the Navy is always in need of Nukes, and there will be people willing to jump through hoops to try and get you in. If your transcripts & test scores indicate you have a high probability of making it through the training, and you convince them that your past behavior will remain in the past, I think you definitely have a chance of getting waivers.
