They have a few benefits: they start with a huge resource of cash, as well as 2 battle victory tokens, plus several technologies already researched (Plasma Cannons, Gauss Shields, Fusion Drives). Their ships are generally of standard design, although their Dreadnaught does have +1 power source.
The downside, though, is huge. They start with 2 less influence discs than the other races. That means that while the other races might normally have 3-4 actions a turn, once your cash runs out you’re down to 1-2.
As such, the strategy seems to be to try and quickly expand your economy (to gain more actions) and really make efficient use of your actions.
One tactic I wanted to try (which didn’t quite pan out, as I was playing them in a 9 player game) was to try and take 6-7 actions in the first turn, using them all to explore tier 3 sectors. Tier 3 sectors have a restricted number in the game, so the theory would be that by claiming more than your share of them, you would be denying them to your opponent.
Part of the difficulty of such an approach would be colonising them, as you only have 3 colony ships to use each turn. Of course, you could refresh those ships with an Influence action. However, as mentioned above, as Eridani you really want to make efficient use of your actions, so “wasting” one on an influence action is not necessarily ideal.
My plan was to only colonise worlds that provided Economy, to try and bolster my number of actions in the following rounds. There are problems with that, though. For starters, you need to claim a system (by placing one of your already scarce influence discs on it) before you can colonise the planets. The other issue is that many of the tier 3 systems are sparse on worlds – they may only have 1 colonisable planet, or none (and just a discovery tile). If you are spending 1 influence disc to gain 1 economy, it’s getting close to a zero net sum gain.
To really get back into the game, I think the Eridani need to get Advanced Robotics, Quantum Grid, and probably Orbitals as soon as possible. The difficulty with Orbitals is that you need minerals to build them, and the Eridani home system doesn’t start with any mineral worlds. Also, those things cost Science resource, and the Eridani only start with 2. With a 3-1 exchange rate, you can probably buy Advanced Robotics if it’s there on the first turn (2 science, 9 cash = 3 science, 1 discount for existing tech), but you can’t afford Quantum Grid (15 Science with the discount for existing tech). And, as anyone who has ever played Eclipse will tell you, you can’t count on the tech you want being there when you need it.
Plus, to really take advantage of your starting technology (mainly the Plasma Cannons), you need to research a better power source for your ships. That’s a lot of stuff you need to research, and that’s tough to do with limited actions and limited Science resource. Plus, you’re then investing in a less-than-optimal technology (plasma cannons).
In terms of efficient use of actions, the Eridani really like big ships (I read an article about Eridani loving Dreadnaughts, and I don’t disagree), because it means you can move them relatively cheaply. The problem with such ships though is that they leave your systems open to being swarmed (enemy leaves 1 interceptor to pin your Dreadnaught, then sends their other ships through to total your systems). Also, by taking fewer actions, your opponents are able to react after your actions to whatever you do.
All in all I think the downside of the Eridani is just too much to overcome. I found myself spending a lot of energy trying turn around my economy, which ended up meaning my military was underpowered.