By the way, your parents can not stay in US longer than the I-94 expiration date unless they file I-485 before the I-94 expires.
Follow up question:
Their priority date was 8/2/2002 which is 1 day behind the current listing (what's the odd).
-Then, they can not file I-485v in May 2015 (useless to file it).
I know you said they cannot stay in US after I-94 (6/26/2015), but what if they can't get the current date by June, do I have to file B2 visa extension in June and then file 485 in July?
-Depends on when the priority date is current. The principle is that they have to have a legal status to file I-485. They can not file I-485 even if when the B-2 extension is pending(after the current I-94 expires). If their B-2 extension is approved and the priority date is current, then they can file I-485.
From my understanding B2 visa ext takes 45 days, that means they will be out of status from 6/26/2015 - whenever b2 ext is granted.
Or, from some previous posts here, they can file 485 while in US regardless of their Visa Status or I might be mistaken here.
-Not true for your parents' case because your father is sponsored by his sister, and your father is not the immediate relative of his sister (US citizen).
Immediate relative of a US citizen = spouse, parents, or child < 21 years old of the US citizen, who have special advantages in immigration.