I don't really play the NR at all, but I play a lot of the EoTH. For ground battles, they get two very strong units, though the gilzean is only one at the initial tech level.
The Gilzean is an almost comically over powered super tank squad, off the top of my head I don't know if any other faction that has a unit that will win a one on one fight (by one on one I mean unit on unit, and gilzeans are a three tank unit) other than potentially artillery or air units, though they can still get taken out by turbolaser turrets. THeir main advantage is that they have total freedom of fire even while moving, so even if they are driving by something, they can still blast it. Combine that with their high damage and decent movement speed and you have one very good ground unit.
The other strong ground unit they have is the airstraeker, which is a flying unit with very high speed, good fire power, and the ability power to weapons. Airstraekers are very powerful units, but they have much worse AI even when directed to do specific things so unlike the gilzean, efficient use of them requires a large amount of micro managing. One of their biggest issues is that if directed to attack a unit, the maneuvers they preform if their initial run doesn't take out the target does not usually bring them far enough away from their target to line up on it again, so they end up flying around it getting shot without firing back, but this can be overcome with sufficient oversight.
In space, the EoTH has a very nice mixture of ships with some clear strengths and only one notable shortcoming. Aside from their lack of a super ship, which they lack for story reasons(and in my opinion game mechanic reasons), they have one of the most powerful non super ships in the game, and they also have under current iteration, the most point efficient capital ship in the game (capital ships is not including heavy frigates or below). The phalanx is one of the best non super ships in the game, it has high health and shields, very very high weapons output, and non destructible engines, this combined with the EoTH's shorter retreat time makes it a very powerful choice for hit and runs.
The Efficient ship I was talking about is the Ascendancy class star destroyer, which in addition to very good weapon damage, costs only 3 population points for a capital ship that can rival almost all 4 pop point ships in health and damage (I beleive the only 4 pop point ship that outright beats it is the Tector) and in addition, it releases all 4 of its fighters right away giving it one of the highest number of field-able fighters per point in the game, allowing a fleet to pop in, and drop 52 fighter squadrons for hit and runs is incredibly useful in a lot of cases. They do however fall off in longer fights or against enemy fleets with decent anti-fighter capabilities as they only have the 4 squadrons they drop at the beginning. They also have destructable engines unlike the other EoTH capital ships so they may not be appropriate for all engagements, and can be substituted for the heavy frigate chaff in those cases.
The chaff is I think the second most powerful heavy frigate in the game, falling behind the VSD I and being roughly on par with the crimson command VSD II. It has high firepower, and decent shielding and armor, but most of its damage is from ion cannons, it does better against shields then hull, but its missiles give it a little anti fighter capability and its power to weapons means that against any other frigate, its shields will last longer, allowing you to win even against the more powerful VSD I ships, and its maneuverability can sometimes allow it to even single handedly take on larger ships and win.
For general space strategy, the EoTH has a disadvantage when it comes to defense because they lack a planet based defensive weapon, though they have two very good space defense stations. Even though the Visvia is very powerful, in most defensive cases, it performs considerably worse than its cheaper counterpart. It has a lot of firepower, but it will lose to even two capital ships often without taking even one out if it has no other support, on the other hand, a ordo defense station drops a large number of fighters, and in combination with a shipyard, can give you a large enough force of fighters to sometimes take out multiple capital ships. It is worth noting that if you are being attacked mostly by frigate fleets and no capital ships, the visvia can be a strong defense against them.
Offensively, The EoTH lacks a super ship at all tech levels, so the hit and runs with those that are so effective with other factions are something they have to try to match with lessor ships. a fleet of phalanx class ships dropped in the right place can take out shipyards, golans' or out of place ships and often retreat with out losses, and then come right back to do it again. Syndics and chafs also work in this role as they have indestructible engines as well. Ascendancy star destroyers have destructible engines, but their ability to drop 3 fighter and one bomber squadron for only 3 population points lets them be dangerous on hit and runs as well.
The one thing to be aware of is that their are a number of ships for the EoTH that are essentially traps, and a couple that while not traps, are very niche. The Chaf is a very good ship but expensive for a frigate, the budirech is a weaker cheaper version that has the same population cost, and in most cases is not worth it as 3 budirech ships will lose to 2 chafs and cost more. of the frigate class, the Chaf is the only really strong ship the EoTH has, the Auriette is a decent carrier, but for its cost you might be better off splurging a bit and getting a Ascendancy instead, and if you are low on capital ship construction capacity, the chaf is generally a stronger choice. THe auriette is a decent choice in mass for defensive fleets, as in combination with ship yards and ordo defense stations will give you up to 59 fighter squadrons that are all garrison units, but the ships themselves are fragile so thy are generally outclassed in attack fleets.
The two anti fighter corvettes are both vital to both offensive and defensive fleets as no other EoTH ships have good anti fighter defenses, though a couple have missiles giving them at least a chance to fight back (but with only a tiny number of missile hard points, this hardly qualifies as a defense). The EoTH fighters are decent, but will lose in most cases to the carrier heavy NR and PA fleets unless you have some corvettes for taking down the fighters.
Other than the interdictor, the only other frigate the EoTH have that is even worth mentioning is the Kariek. At one population point and coming with a fighter squadron, it makes a decnet alternative to the anti fighter corvettes as anti fighter support, and it can also make itself a fairly powerful and quick to build disposable fleet with the ability to do quite a bit of damage. Every other ship in the EoTH is pretty hard to find a good use for, not that they are all bad, but with the couple of spectacularly powerful and efficient ships that the EoTH has, the ships that are below average like the awesome but incredibly weak nuruodo and they end up becoming trap choices by comparison.
Because I really like the Nuruodo, I'll explain its issue. It is a ship that seems best designed to function early game, because it is not efficient enough per population point to choose it when you have plenty of money later, but because of so so maneuverability and its interesting firing arc, it ends up being very bad for defense with the limited control set up in the game. Early game, as EoTH, you have a serious lack of safe expansion ability because you start with pretty much the smallest territory in most of the GCs, and the lowest income, combined with the fact that both of your neighbors have at least one SSD available it becomes imperative to fortify to at least some extent while shoring up your income. because of this, the early game opportunity to make use of the ship while it is still good (its good when you are poor and your enemies are have fewer capital ships and heavy frigates, and it is bad against heavier ships and really bad against fighters) ends up being extremely limited. to make matters worse for it, by the time you are ready to expand you usually have enough money to just make more expensive but more efficient ships instead. Even on from the ground up where the poor phase lasts for a long time, its too fragile to make it a good choice over the more expensive ships since they are far sturdier.
EDIT: Even with paragraphs, this still looks like a wall of text.