How do I push the 'Holy Roman Empire' out of Britain?

This answer deals purely with the combat situation.

What are your retinues, and how many do you have? Unlike your levies, you have complete control over the unit composition of your retinues, and can construct them to abuse the combat system to destroy armies multiple times your size (its glorious watching 10k dudes consistently murder the crap out of a 30k doomstack).

In short, an army consisting of many diverse unit types is eligible to RNG a larger number of different combat tactics, and furthermore, those bonuses the combat tactics provide only apply to a small portion of the army and may even provide negatives to other portions of your army. Thus having a focused retinue concentrated in one army (or a single flank of an army if still small) constructed to optimally select combat tactics is a massive force multiplier.

Given that the Irish culture retinue sucks, go with a setup of 4:3 ratio of Defensive:Skirmish retinues (this is the generic version of arguably the absolute best retinue setup of 1:2 Longbow:Defensive under the same theory). This leaves you with a basic building block of 3500 units for 5000 retinue points:

• 2000 - 57% Archers
• 1200 - 34% Pikeman
• 300 - 9% Heavy Infantry

This leaves you in Skirmish only eligible for Volley (Generic Skirmish doesn't really enter in any consideration) and if a Welsh or English leads the flank, Massive Longbow Volley, both of which give considerable bonus to your predominant archers.

I don't want to fill this answer with calculations, but at a minimum, this one block of 3500 are dealing 32k+ damage (2000 archers x 4 attack x 4 multiplier for Volley). A fully mixed army of the same size would probably deal on the order of 7k on average (this number is out of my ass).

Given that you likely won't need to face 90k at once since the HRE will have to ship their army over piecemeal, you can then destroy their armies one by one while minimizing losses due to superior troop mixtures.

Oh, and one more thing - don't forget you can assassinate the leaders of a battle mid-battle >;)

Aside - in a forum game I was participating in, I did run the numbers and gave this advice in response to a bad battle (Horse Archers being the retinue in question):

Ouch. That sucks. Looking at the composition, their army outclassed us slightly. Converting to retinue points, 16813 worth of units vs 16161, with considerably more heavy infantry and considerably less light infantry (which honestly should be worth less than 1 point - they get almost NO tactic bonuses).

We had basically no melee presence compared to them - if we couldn't win in skirmish, we wouldn't win, and our flank composition as shown was not suited to forcing a smashing victory in skirmish either (not enough archers or horse archers, too many light infantry).

Something that may have helped considerably though - keep the retinues in one flank. Diluting them across all our flanks is suboptimal - mixing with other units will drastically decrease their effectiveness. I think it often makes sense to run a smaller pure-retinue flank (as long as it isn't too small). So in this case, I think a 3850/3850/2300 actually might have done better - likely more damage on average than a 3333 mixture due to restricting the available tactics pool.

Here's my analysis of a pure Horse Archer retinue:

Skirmish Phase:
41%        Harass                  3.87/4.48
41%        Swarm                   9.44/4.48
18%        Harass Swarm            9.06/4.48
           Average Unit (SD)       7.09/4.48 (2.68/0.00)
Special    Retreat and Ambush      14.10/4.48

Melee Phase:
50%        Retreat and Ambush      NA
50%        Raid                    9.53/3.52
           Average Unit (SD)       9.53/3.52 (0.00/0.00)

While there's no frame of reference for this, I'll just say that their Skirmish on average is pretty good (even without R&A) and melee crap. Mixing in units will expand the possible tactic selection pool, basically making everyone in the flank worse, and you're almost never going to roll Retreat and Ambush.

For the 3333 mixed (the flank composition as shown) vs 2300 pure
example, that means:
3333 Mixed Flank - 1.71 average attack* x 3333 = 5700 total damage
2300 Pure HA Flank - 7.09 average attack x 2300 = 16300 total damage, worst case (Harass tactic) 8900 damage