Since he is not a US citizen, after we are married, will I be able to apply for H4 dependent work visa and gain a legal status?

Unfortunately, you cannot benefit from a marriage to an H1B visa holder: to change your legal status in the U.S. you need to have a status; yours ended about 10 years ago. At this time, the law makes you ineligible for any status in the U.S. until you return to your country for 10 years. One exception from this rule can be granted if you marry a U.S. citizen. Other exceptions exist but they all require petitions by your U.S. citizen or permanent resident spouse, parent, or child, and are very difficult to obtain.