What really happened at the end of Stone Ocean? At the end of Jojo Part 6: Stone Ocean, did Emporio get sent to a parallel universe? Is this the same universe that SBR and JJL then take place in? The wikia says that the universe is reset. What really happened? I'm so confused...
Some years ago I shared your confusion, and I kept thinking and thinking until I found an answer I was satisfied with.
I also wrote this "answer" in an italian forum I was part of at that time.
To be fair, it did not receive very much attention, but I want to translate it because I think it could be of some help (I doubt it to be correct because I believe H. Araki's brain creations are too much for anyone to understand).

Here I go:

Father Pucci makes the universe collapse by means of the powers of his Made in Heaven.
Then, the universe rises again for another cycle of life.
The interesting fact, which H. Araki himself explains to us, is that this new cycle will be exactly the same as the one before except for the fact that all the living beings that are actually alive when the collapse takes place will return in the second cycle of life with full knowledge of their future. 
This consciousness of the future is how Father Pucci believes happiness will be achieved by mankind.

The new history of the universe will be written in such a way as to preserve the faith of who was alive before the first collapse operated by Father Pucci through Made in Heaven.
Details will obviusly change, but the main part of their faiths will be unaltered.
As for the deads, something similar happens in the sense that their new lives will be somehow "connected" with the lives of those with whom they were connected in the first cycle, but there will be no clear knowledge of their faith for them.

It is clear that Father Pucci is the only living being which is outside of the "written faith", and he can move arbitrarily in the cycle of the new universe because of the gravitational powers of Made in Heaven. 
Since Father Pucci knows that Emporio is alive before the collapse, he decided to close the  situation once and for all, and goes back to the prison (during the second cycle of the universe) in order to kill the little guy.....and this is where Father Pucci makes his big mistake.

Emporio manages to survive Father Pucci's threat precisely because Father Pucci is immune to Made in Heaven powers.
Indeed, we know that the details of the lives of who was alive before the first collapse may change, and this clearly allows Emporio to have some kind of mental and physical freedom with which he is able to think to a plan to kill Father Pucci.
Furthermore, we know that Father Pucci's faith is completely open, there is no predestination for him because it is his will to actively keep using his powers the reason of everyone else's fixed faith.
This means that, even if Father Pucci can litterally decide the faith of the universe, nothing prevents him from dying like the idiot he surely does not want to be.

Then, he dies, of course.

Before dying, Father Pucci decides to accelerate Time again hoping to prevent the result of Emporio's plan (his death) before it actually realizes.
All he succeds to do is to set a third cycle of the universe, a cycle of which he will no longer be part of.
However, Emporio was alive at the time of the second collapse, hence, he will be fully conscious in the third cycle, and thus he tries to reconnect with the group.
He finds Irene and Anakis, the "alter-ego" of Jolyne and Anasui, who, however, do not have Emporio's knowledge of their faith and are not able to remember him (they were dead before the first collapse).

In this third cycle, Father Pucci is no longer there because he died in the end of the second cycle, and thus we may safely assume that there will be again a lot of freedom for everyone.
Accordingly, I believe that SBR takes place in this third cycle, because, if it had took place during the second cycle, there would have been Father Pucci somewhere in the universe, and this would have made the plot of SBR meaningless with respect to the "fixed faith" imposed by Made in Heaven.

Now that I wrote it again, I feel better.
Please, forgive my english and let me know what you think.

Remark
At the time of my writing now (26 January 2019), I have not yet started reading JoJolion (part 8), hence, I do not know what happens there. 
The following edit has been suggested by someone who is reading JoJolion, and I thought it could be meaningful to add it because it seems to disprove my "theory" on the end of Stone Ocean.
However, I reserve my right to re-edit this answer once I read JoJolion and I have thought about it, and I warn people who have not read JoJolion that the following suggested edit contains information that may be perceived as spoiler.
End Remark

Peer edit: 
In JoJolion (part 8), the theory that the Steel Ball Run universe takes place in a cycle of Made in Heaven was disproven, as the complete Joestar family tree is shown, and there is no Jotaro nor Irene. 

This is because the Steel Ball Run universe is a completely different universe. The third cycle of Made in Heaven is its own universe.
The SBR-verse and Ireneverse have no correlation whatsoever.