H1 B Visa
The H-1B is a non-immigrant visa in the United States under the Immigration & Nationality Act, section 101(a)(15)(H). It allows U.S. employers to employ foreign guest workers in specialty occupations.

The regulations define a ââ.¬Å.specialty occupationââ.¬Â� as requiring theoretical and practical application of a body of highly specialized knowledge in a field of human endeavor including, but not limited to, architecture, engineering, mathematics, physical sciences, social sciences, medicine and health, education, law, accounting, business specialities, theology, and the arts, and requiring the attainment of a bachelorââ.¬â.¢s degree or its equivalent as a minimum. Likewise, the foreign worker must possess at least a bachelorââ.¬â.¢s degree or its equivalent and state licensure, if required to practice in that field. H-1B work-authorization is strictly limited to employment by the sponsoring employer.

Can H4 legally work in US?

NO.

NO but they can try to apply for Jobs and if they get it they can apply H1 B as the quota is till open.