What document do they need to file to change his status if his I94 has no expiration date?

I am sorry, but unless your sister in law is either a legal resident, or an alien in valid non-immigrant status, she may not be able to renew her driver's license in several states including possibly New York. If she has been in US for the last 10 years and has no immigration case pending, she is out of status. Her first option is to consult with an experienced immigration attorney to assess immigration options in United States. It is only when she is in legal status or has filed and has pending a meritorious adjustment of status application will the Dept. of Motor Vehicles, "DMV" will renew her driver's license. In conclusion, because the rules are not uniform with respect to this matter. While some states refuse to issue driver's license to illegal immigrants (Washington State) while some other states like Arizona do not).Your sister may want to conduct further inquiry on this issue with respect to the applicable rule in the various states.

In what status did they enter 10 years ago that their I-94 does not have an expiration date. Also, what is their current immigration status in the US?

It depends, but it appears as if your sister and nephews/nieces may already be out of status, especially if they entered the US merely as visitors and it has been 10 years since they left. However, your nephews and/or nieces may be eligible to apply for Deferred Action for Childhood Arrivals to get temporary work permits, which can be used to renew your nephew's driver license, if they entered the US before their 16th birthday and are currently enrolled in school or have graduated from High School.