"нечто" IS the nominative form. And it is used as an indefinite pronoun which means "something":
Там происходило нечто странное. - Something strange was going on there.
You can. "нечто" is the same form for both nominative and accusative. And, as I said, it means "something":
Сегодня я узнал нечто новое. - Today I've learned something new.
I'm afraid I do not understand this question. "нечего" is the genitive form. So, your question (about genitive case being used for nominative and accusative) does not make sense.
Please provide a more specific example, to make it clear what you mean.