You'll need to ask China Eastern at check-in, and double-check the tags they put on your bags. On this sort of connection, policy is actually more under airport control than airline control. If NKG policy is for all international transit passenger connections to pick up and recheck, you'll need to do that. But if NKG allows intl transit passenger bags to be automatically routed through, you may be able to avoid fooling with them. I don't have any specific data points from travelers who have done intl transit through NKG, so unfortunately all I have to offer you is generic.
Assuming NKG allows auto-routing, the second wrinkle is whether MU and OZ have an interline agreement. They are not in the same Alliance so this should be checked with MU also. If they do not, then you'll be picking up bags and rechecking for sure.
I do not know what the Minimum intl-to-intl Connection time is at NKG, but 1:20 seems to be realistically OK if everything is on time, but tight if that inbound from HKG is delayed by a significant time. It's a bit of an odd way to go from HKG-ICN, to be sure.