MineOS is not an "official" TurnKey appliance, hence why you can't find it here. I did have some discussions with William Dizon (the lead dev) some time ago about integrating it into the "official" library but it stalled (TBH I don't recall why OTTOMH). You can find the MineOS forums here: https://discourse.codeemo.com/

So although it's probably irrelevant, FWIW all the appliances can be found here and the front page has a search bar so you can (hopefully) find what you're after...

TBH I have no idea about "forge automatic installation" (I assume it's a minecraft thing...). But I can talk to the OpenJDK thing, at least from our perspective: There are 2 primary reasons:
1. Unlike Java6 (and prior); as of Java7 the differences are fairly insignificant. Oracle actually support OpenJDK and use it as their "reference build" (i.e. they extend on it but use it as the base for their JDK). There are some people that suggest that Oracle JDK is still in some way superior but I am yet to see any empirical evidence of that. Obviously there are edge cases where the developers use Oracle JDK for development which might then mean that specific software needs Oracle JDK to function; but generally open source devs these days use OpenJDK; so there should be no need for the Oracle closed source version.
2. Most importantly for us (and I suspect MineOS too) OpenJDK is open source and can be freely distributed. Whilst Oracle JDK includes the open source JDK, it is proprietary (i.e. closed source) and can not be legally redistributed. So distributing an ISO that includes Oracle JDK is illegal. There are ways around that (e.g. an install script which the end user agrees to on first boot) but we do not believe that there are any significant reasons not to use OpenJDK so we don't do that.