So a brief review of all the factions and their control. Blue is the Jon-Petyr alliance, although I am taking it for granted that the Riverlands is held between Littlefinger and Edmure and not any surviving Freys. Red is the Lannister control and their allies, not including Euron (yellow) because Euron may or may not be anyone's ally. Black is the Danaerys/Olenna/Snek alliance, including Magister Illyrio, and Green is the Iron Bank of Braavos who are aligned against the Lannisters but haven't picked a replacement side.
Northern strategy is rather simple, garrison the Wall (focusing on Castle Black and Eastwatch by the Sea), garrison Karhold, Dreadfort and Winterfell, all to focus on the White Walkers approaching from the North. The only complication is Littlefinger and the Vale forces, what with the Vale forces not having any reason to be in the North and Littlefinger faffing about.
Lannister strategy is to eliminate the Tyrells and replace them with the Tarlies, ignoring the Dornish to instead focus on the three main threats:
1. The lannister forces starving to death or rebelling from lack of supplies. Taking the Reach and replacing them with loyalists solves this issue.
2. The Targaeryan dragons.
3. The Dothraki Horde. The Dothraki horde will not be easy to defeat in a pitched battle, possibly beyond the capabilities of even a Lannister coalition that included the Reach. However, if they were to force the Dothraki into siege, the Dothraki are not experienced in siege warfare and would have extreme difficulty feeding all of their horses and men - as winter approaches, their casualties will be immense. Having the Dothraki without, will also guarantee internal stability within - the Westerosi will fight to the death knowing the Dothraki are at their door.
Realizing that stranding her army on Dragonstone was a poor life choice, Danaerys took Tyrion's advice to attack Casterly Rock. The Reach's Redwyne fleet and Danaerys's Meereneese fleet sailed forth with her Dothraki and Unsullied, making for Casterly Rock with Tyrion's knowledge of the Casterly Rock sewage system likely going to make a major impact (especially notable since the Unsullied have conducted won sieges of fortified cities this way before). Her Ironborn, Dornish and Reach ground forces would then launch a siege against King's Landing directly, using the ships of the Iron Fleet and the Dornish Fleet, cutting off all lines of communication between the Iron Throne and their armies.
Something immediately concerning about this plan is that it ignores the Royal Fleet. Tyrion, who oversaw the State's budgeting when Cersei was drastically emptying the Kingdom's coffers to rebuild the Royal Fleet from scratch with several top of the line warships, would know this - and for whatever reason withheld this information from Yara and Danaerys. Tyrion, who oversaw the defence of King's Landing in the Battle of Blackwater Bay, withheld all the information he knew about the defences
he designed from Danaerys and Yara.
In the show we see three major characters who can appropriately be called Naval Strategists or Commanders. Euron, Yara, Tywin and Stannis.
Tywin, Euron and Stannis are all interesting because they or their fleets all fought before in naval engagements. During the Greyjoy Rebellion, Euron is one of the Greyjoys that launches the fire attack which destroys the Lannister fleet at Lannisport. Stannis Baratheon is the one who is then sent with the Throne's Royal Fleet to clear the Iron Islands, and he destroys the Greyjoy Fleet. Stannis surmises that the Greyjoy fleet was composed of effective raiders, especially when launching surprise attacks, but were not really staffed with Captains or equipped with ships built for fleet engagements.
It's useful then comparing how Stannis entered Blackwater Bay vs how Yara entered Blackwater Bay.
Yara and Stannis were both seasoned naval commanders. Yet the former is a reaver, the latter is a soldier. The former is used to launching marine assaults and retreats, the latter is used to destroy fleets and win campaigns. When Stannis launches his assault on Blackwater, he attacks at night with a vanguard scouting ahead, the main body approaching and a rearguard outside the Bay, utilizing tactics intended to destroy enemy ships and clear the coastal fortifications. Yara launched her assault at night, during a storm into poor visibility, with no scouts or rearguard, with ships that possessed no archers, crossbowmen or ballista, being all equipped for launching raids. Yara did not post sentries and was distracted, entertaining Dornish nobility instead of overseeing the most critical battle towards winning the Iron Throne.
Simply put, if Euron was not there, then it's significantly likely that Yara would have encountered the Royal Fleet, another Wildfire gambit or the Coastal Fortifications and suffered tremendously for it. Her fleet probably could've suffered horrendous losses and still won, however it is puzzling why Tyrion withheld such vital information or why Yara was so excessively careless (being below deck having sex and drinking is not the place you want to be when you're conducting military maneuvres).
Euron seems to be having fun, and I can only guess that he must've known Danaerys's Iron Fleet was approaching - I'm guessing he noticed their fleet on his way past Dragonstone, avoiding detection somehow (or I suppose, he was waiting in Blackwater all this time, and received reports from ships or units stationed along the Stormlands - or even from Lannister forces themselves). Euron then conducted an attack similar to the one he conducted at Lannisport, combining it with the strategy Stannis employed against him so many years ago. Most of his fleet are off-screen (in fact as far as I can tell rewatching it, the entirety of Euron's fleet is off-screen launching fire-munitions), with only Euron's flagship charging into the fray with the express purpose of capturing the nobility aboard.
Most interesting of all will be seeing what Euron's next move is. Marrying Cersei does not seem to be Euron's end goal, what with Euron's express end goal being to marry Danaerys and conquer the world with her dragons. If Euron had destroyed all of Danaerys's fleet, he would've been in position to demand marriage in exchange for his fleet, but Danaerys still has the Redwyne and Meereneese fleet at her disposal (and more importantly, on the other side of Westeros where they are safe).
I really can't guess how Euron plans to springboard from marrying Cersei to marrying Danaerys, unless Euron plans to marry Cersei, usurp or kill her, then propose a marriage proposal to Cersei as King of the Iron Throne..