It's pretty hard to give good Oblivaeon advice, so much strategy is extremely situationally dependent and I feel like the ability to improvise a strategy based on board conditions are much more important here then they are anywhere else in Sentinels. Here are the best tips I can give for now, hopefully as I improve over time I can give better advice (I'd love to get good enough to write an Oblivaeon guide at some point).
General:
1. I usually pick my starting heroes and environments at random for a little extra Challenge but I strongly recommend bringing at least 4 heroes. Oblivaeon is easiest for 5 hero teams and is very difficult for 3 hero teams.
Phase 1:
1. As a general rule I try to get past the shields as quickly as possible. I know a lot of players worry about flipping him too fast, but to me making sure you live through phase 1 successfully is more important than anything else. In around 25 or so games of Oblivaeon, I only recall losing once after successfully getting past the Shield and I gone on to win once or twice after failing to get past the shield in time.
2. The second most important thing to do phase 1 is work on completing missions. 1 tip is it's generally preferable to take on a mission even if you can't complete it than to shuffle the mission deck. Taking on the Mission means that it cannot end up back on top of the deck by an unlucky shuffle and it means you'll have something to trade with other player's if one of them pulls a Mission they can't compete but you can.
3. Whenever possible, destroy Aeon Locus so that Oblivaeon won't get extra plays off them. These guys are by far the most dangerous Aeon Men and are often more important than Scions to damage.
3. A lot of Oblivaeon' shields are highly positioning dependant. It often makes sense to look at the Oblivaeon and Scion decks (assuming you're playing digital) to see what cards could be played that would screw your plans up and trying to minimize that risk.
4. When choosing a new hero after 1 of yours is incapacitated, base your choice first on what hero can help you with the shield and second on what rewards you had with the incapacitated hero that the new hero may be able to utilize.
Phase 2:
1. If you successfully beat Oblivaeon's first phase the beginning of phase 2 is the best time to farm up some rewards. If you get some good rewards in the first 2-3 rounds you'll probably be able to take out most of Oblivaeon's 180 HP in the next 1-2 rounds.
2. Alternatively, you can choose to split your team between the 2 battle zones and focusing on Scions instead of Oblivaeon. You'll lose an environment at the end of the phase but if you can keep the devastation token count down you can be in a strong position for Oblivaeon's final phase.
3. If there are Aeon Men in play pay attention to the order Oblivaeon hits them. If you can order the hits so that the Aeon Loci are healed by Thralls so that Oblivaeon doesn't take out the Loci, it's incredibly worthwhile to do so. It can also be worthwhile for avoiding Aeon Vassal and Warrior "on destruction" effects.
Phase 3:
1. If you have the ability to block villain plays this is the time to use it. Otherwise it's important to remember that Oblivaeon will only play extra cards if you're in his battle zone. Only heroes that can do enough to Oblivaeon to outweigh the downside of his plays should confront him.
2. Unlike Phase 2, Phase 3 does not generally punish you for damage immunity or preventing villain damage.
3. If Voss is around, consider killing him if you have a means to overcome his damage reduction. He much less scary now than if he flips.