Let's talk about NXT first this week, and the WWE observations can be folded into Extreme Rules predictions after that.
The big doings in NXT are the main title, where a feud between Finn Balor and Samoa Joe has largely taken place at house shows for some reason, and has been so intense that their match in three weeks will be the first ever NXT steel cage match "to protect the NXT fans". No idea where they're going with this but they may be giving Joe his traditional two wins over the champion before the champion moves to the main roster.
Nia Jax beat Bayley definitively this week, which probably means Jax-Asuka at Takeover. What I don't know is, what this means for Bayley. Sasha Banks is essentially off WWE TV at this point while Becky Lynch, Charlotte, and Natalya take up the attention the WWE has decided the audience has for women's wrestling, and the scraps are taken up by the debuting Dana Brooke (thanks to an Emma injury) and whoever happens to be around to job on TV. This is not an environment conducive to a Bayley debut, but being out of the title picture (barring the "rematch clause" loophole - triple threat at Takeover?) isn't great for her either.
The Revival get their tag rematch against American Alpha in three weeks, but there's no story there and no buildup, just a straight rematch from one PPV to the next.
,.EXTREME RULES PREDICTIONS:
Pre-Show: Dolph Ziggler vs. Baron Corbin (No DQ):
Who cares? The WWE doesn't. They forgot this feud was going on for three weeks and only remembered on the Smackdown before Extreme Rules. I'll say Corbin, because Ziggler's miserable situation demands it.
Karl Anderson and Luke Gallows vs. The Usos (Tornado Tag):
Anderson and Gallows will win to keep their debut momentum and maintain the illusion that Styles has a chance in the main event. There may or may not be Styles and Reigns interference depending on how much they want to make this match like all the other times these two teams have wrestled in the past month.
Chris Jericho vs. Dean Ambrose (Asylum Match)
For the first time ever in WWE, a cage match with a bunch of weapons at the top of it. WWE calls it's version of TNA's "Monster's Ball" and "Asylum Match" in honor of Dean Ambrose, so there's no way they'd have Ambrose lose his own inaugural signature match, and that should overcome Jericho's relative unwillingness to put people over in his latest WWE run.
Charlotte vs. Natalya (Women's Championship, Submissions, Ric Flair Banned From Ringside):
The question for this match is, in all probability, who will drop the belt to Sasha Banks at Summerslam? Which depends on whether Sasha Banks will be a face or heel. She plays generally heel, but she'll get face crowd ractions on account of being Sasha Fucking Banks. I'm gonna say Natalya, but I'm not confident with this prediction.
The New Day vs. The Vaudevillains (Tag Team Championship, No Extreme Stipulation For Some Reason)
The New Day retains. The Vaudevillains are being done a great service by being in the match at all, and there's no reason to have The New Day chase the belts. On a related note, props to The New Day for having their time machine go back to Kofi Kingston's original intro and Jamaican accent before continuing on to the Bygone Era on Raw this week. Funny bit.
Jalisco Vs. Rusev (US Championship, No Extremeness)
Rusev has been dominating Kalisto on TV of late. Booking logic means he'll retain, but John Cena's coming back soon, and has history with both the US Title and Rusev and will need something to do. So I'm going to call for a title change here and Kalisto can go back to being wasted in tag matches. There's a rumor flying around that WWE wants to pair him with a woman, which would be a great idea in Lucha Underground and an idea WWE will utterly botch if they try it.
Sami Zayn vs. Kevin Owens vs. Cesaro vs. The Miz (Intercontinental Championship, Fatal Four Way)
Cesaro winning the belt here is literally the only outcome that makes sense. Owens and Zayn have unfinished business that this match can help move forward. The Miz is a placeholder champion who won the belt from another placeholder champion. Cesaro could do a lot with the belt, and it's long past time he got a chance to.
AJ Styles vs. Roman Reigns (WWE Heavyweight Championship, Extreme Ruiles):
Roman Reigns wins. I suspect the WWE will give Styles the big belt at some point, but this is not that point. The Roman Reigns Experiment will continue until morale improves. AJ deserves a better opponent to beat for the belt anyway. This will not be a five star classic match of the year candidate, either.
Overall, it should be a decent enough show, with at least four solid to very good matches (Women's Championship, Tag Championship, IC Belt, Asylum) and only a couple of likely duds (Main event, Main-event-related-tag match).