I am not sure about Indian laws on citizenship and immigration.
In Japan, once you are married, your husband can stay in Japan with a spouse visa, and would be eligible for a permanent visa after 5 years. After that, he could choose to become Japanese.
However, it's important to know that neither Japan or India accept dual-nationality, which means if you take on the Indian nationality, you are no more Japanese and if your husband chooses to become Japanese, he loses his Indian nationality.
Children normally have both nationality until the age of 18 (or 20 in Japan ?), t which time they must choose one.
Have you ever been to India ? Where do you intend to live ?
Another good thing to know is that if you have children born in the US, they would be eligibile for 3 nationalities : Indian, Japanese and American, as anybody born in the States can become American.
If you plan to live in the States, then marriage doesn't help any of you to stay there, but it might be easier to get American citizenship than Japanese or Indian ones.