This is an ingenious thread.
OK - I'm leading an Akaviri D-Day.
Coming from the east, I have four primary concerns:
1. Landing in an area where I can bring overwhelming force to bear against any potential defenders
2. Keeping my logistics train as short as possible so I can bring in supplies and reinforcements
3. Landing in an area that is suitable for naval assault operations
Hands down - the choice is southern Morrowind.
There is arable land that can provide supplies short and long term, pasture for cattle and cavalry, and light defenses, with the overwhelming majority of Redoran defenders in fortified positions to the south, facing Black Marsh.
One can expect House Redoran to lead the organization of a counterattack, but with the other houses scattered and weakened, and the tribunal (along with Vivec) long gone, there would be no chance for the Dunmer to eject an Akaviri force.
From here, strategy, politics and maneuver will all be key considerations.
The Nords are a real danger, but with their civil war underway, the run down state of their province and their lack of love for the Dunmer, it is more than likely that they will be inclined to stay out of the initial response to the landings. Their continued neutrality can be greatly encouraged thru a diplomatic mission to Skyrim, with a message that the Akaviri forces have no quarrel with humans, but rather with Mer - both with the Dunmer for previous hostilities and acts of piracy and slave raids (which, even if not true, could be fabricated), and in particular with the Thalmor and their quest to unravel Mundus.
To protect the conquered territory of southern morrowind from further Dunmer incursions, the Akaviri could fortify the approaches from Northwest Morrowind rather easily - there are mountains to the west and the inland sea of Vvardenfell to the east. I would, however, keep the fortifications away from the proximity of the Riften gate in order to not alarm the Nords.
The Argonians can be appeased quickly by the Akaviri forces crushing the Dunmer counterattack - dead Dunmer will earn some subconscious approval from the Argonians. A diplomatic mission proposing a mutual defense treaty against the Dunmer and trade provisions would help as well. It would still behoove the Akaviri to take the Dunmer's evacuated defensive positions, however.
This leaves Cyrodiil to deal with.
Machiavelli recommended that a nation seeking to conquer a territory with weak defenders should first ally itself with these weak defenders against any powerful outside enemy they may have. With this in mind, I would propose to the Emperor an alliance against the Thalmor. The imperials would almost certainly grab at such an opportunity in the way a drowning man would clutch at a straw. While the Imperials waste their remaining strength against the Thalmor, they will nevertheless weaken the Aldmeri Dominion for me before I need to engage directly. Perhaps there will be a way to broker a lasting peace between the Nords and Imperials so that the Nords commit substantial forces to Cyrodiil, thereby weakening both the Nords and Thalmor further.
In the meantime, I will attempt to separate the bonds between the Thalmor and their client states in Valenwood and Elsweyr. There should be already fertile ground for establishing a native insurgency amongst the Bosmer against their Thalmor overlords. The Khajiit will be trickier, unless the Akaviri forces are composed at least partially of Ka Po Tun. In such a case, there ought to be a way to get the Khajiit kingdoms to at least assume a neutral posture.
While the human forces under the Imperial banner contend with the Thalmor, I will need to use southern Morrowind's timber to expand my fleet. It will be vital for my next moves. I will also need to make serious efforts at colonizing Southern Morrowind to increase its mineral and agricultural output, as well as to have a 'native' akaviri base of operations and logistics support on the continent of Tamriel.
Once the Imperials and their Breton and Nord reinforcements are thoroughly exhausted in their struggles against the Thalmor, I will strike directly at Summerset. I'll need infantry and naval basing rights at Cyrodiilic ports that are on or can reach the southern sea. They will be at their weakest at that point. I need to utterly annihilate them so that they have no chance to recover. This will be one of the two key contests.
If I can succeed totally against the Altmer, I will be free to turn my attention completely against Skyrim.
First: my forces will have to gather at the fortifications against northwest morrowind and in northern Cyrodiil.
Second: I will advance thru Northwest Morrowind and take Blacklight. The Dunmer will already be very weakened, but I might as well finish them off for good. My forces in north Cyrodiil will help to fix enough Nord forces defending Falkreath to prevent them from offering much to the beleaguered Dunmer thru either the Windhelm or Riften gates. Nevertheless, I'll need a blocking force at the Riften gate just in case.
With the end of the Dunmer (except for whatever fragments remain in Solstheim), I can now hit Skyrim at will. This will be the second key struggle of the conquest. With attacks at three points - Falkreath, Windhelm and Riften - at least one of those attacks will be successful and can then support the thrusts of either of the other two. After that, it will be a matter of pursuit of the routed forces up to the borders with High Rock and Hammerfell.
By this time, the Ra Gada will undoubtedly be wishing they hadn't been so prideful of their independence. Nevertheless, I will concentrate a sufficient force in western Cyrodiil and drive the majority of my Skyrim forces into High Rock. This promises to be a difficult campaign because of the terrain and approaches, but the Bretons are not many. If the Ra Gada contribute forces to High Rock's defense, it will weaken them in their defenses against western Cyrodiil.
Once High Rock is taken, Hammerfell will be encircled. I'll take the coastal towns and the cities bordering Skyrim's western mountains. All the other Ra Gada will be driven into the interior, where they will wither.
Valenwood, Elsweyr and Black Marsh could play the role of spoilers. My diplomatic efforts and mutual defense and trade pacts with Black Marsh will help forestall that; besides, the southern morrowind defenses built by the Dunmer will still be mine, and southern morrowind itself will be an akaviri province at that point. Whatever the Argonians do will be more dangerous for them than for me. If there is any connection between the Argonians and Tsaesci, I will exploit that to the fullest to make every effort to keep the argonians non-hostile.
With the Altmer extinct, I think I can use the Ka Po Tun contingent of my forces to keep good relations with the Khajiit thru cultural and economic contacts. Furthermore, I will happily sign a treaty with the Bosmer, giving them recognition and freedom in their own province. They should feel grateful for the support given them to free themselves from the AD.
There's a few wrinkles here and there, but by and large this would be the high level structure of my campaign plan and strategy. It's a Divide and Conquer in its purest form.