ei level 4 is decent it should be around 125 - 130 in strength and it can go to all village without wall and residence doesnt matter about population diffrence
I think you want to do this for AFK farming(?)
So,
1 EI level 4 can attack village up to level 2 City Walls (Romans) + level 2 Residence/Castle and populations difference isn't matter.
or
1 EI level 3 can attack village with level 0 Walls + level 0 Residence/Castle with probably at least less than +7% of your population (I don't know the exact calculation).
But I don't think it's worth to level up EI to level 4 early on, it's better to use 2 EI instead. 2 EI level 0 can attack village up to level 3 City Walls + level 3 Residence/Castle and populations difference isn't matter.
http://travian.kirilloid.ru/wa…1p9999u,,,,1U4b#d:w3R3#uU
No need to remember all the calculations when you can just check here.
Also it is totally worth it to spend a few thousand resources more to get the lvl4 done especially early on when you dont have a lot of troops - rather do micro raiding with 1 unit than 2 units so that you can farm more frequently or more players
I think this subject needs more attention 
Too many players dont use this to their advantage. I think all romans, gauls and huns should spend some time calculating.
The purpose of farming with 1 EI is to hit more small microfarms. for that reason you will never have full load and i would say never full load even with 1 horse. So you can easy calculate it.
The investment is around 31.000 to get them to lvl 4. That is a value of 22 horses only, so i would actually make the argument that already after around 25 EI it would be beneficial for you to make the upgrades. Be aware that if you dont spend all horses for microfarming 1,1,1,1,1 you lose the advantage and should have more, but this is theory:)
Hint: 1 EI can actually farm oasis from the begining. For that reason rushing EI might actually be a viable strategy once again in 1x speed because oasis dont respawn first 5 days. After 5 days you are ready to run down the clubmen!
that only applies if you register immediatly after server opens, if you register 2-3 days later there is only limited time left to use the stategy
for raiding oasis in protection, i suggest to stick to legionairs. The investment for EI is too expensive (77.5 legionairs) which makes you raiding nothing for too long compared to raiding with legionairs only.
77.5 ~ 78/2 = 39 in/outgoing raids on oasis just at costs you would make on investing resources in EI.
Not included in simple math, legionairs also take bounty with them which you could use to upgrade barracks lvl and number of legionairs 
I agree in your point It is expensiv! I just tried it out. building 50 legs and then 50 EI. I hope this will give me advantage to farm better when real farms open.
if you dont care about getting a good 2nd village spot....
you will end up spending too much ress on units, then see that 80% uses extension on protection and settle way before you do.
I agree in theory, but i tried it out and it seems like there is only 1 guy in the server i cant beat.
Made 50 legi and then into 50 EI
http://prntscr.com/tbye78
Never losing troops just heavy microfarming(takes a lot of time, and a bit of skill to optimize)
I will get the 2nd village about day 5
not a lot of competition so might be smart move...
i send settlers before 2nd co bonus, so that is proberly 4 days and 22 hours. It seems quite fast compared to the rest of the server. And most important, 1 day earlier than the guys that buy glad helmet 500k silver...wasted:)
Perhaps that is a bad server where oasis raiders are few. In those servers, investment in EIs will definitely pay back. However, in semi-competitive servers and above, it's a very bad investment. The ROI includes 5 levels of stable, at least 2 crop field 5s due to the increase in pop, level 3 smithy, research, and then 1400 res per EIs invested.
All those res could've easily been put into culture points production. I definitely know that in my servers this is impossible to reimburse. But I have seen it get done in local servers with a good location and bad raiders around. But then the path I believe would be EIs straight with no legions by using the warehouse 7 and residence resources
