Learn English – The meaning of “Even if I should”

Let's break these apart.

1. Even if I do X, Y will happen.
2. Even should I do X, Y will happen.
3. Even if I should do X, Y will happen.

Even is being used as an adverb in all three cases, taking the second meaning in the Wiktionary listing:

"Implying an extreme example in the case mentioned, as compared to the implied reality."

So it is saying that "X" is one of the best options I have.

Numbers 2 and 3 are the same construction, where should is being used as an auxiliary verb to form the future subjunctive. This indicates that X is something I am only hypothetically interested in doing, just for the sake of argument. The indicative mood of number 1, by contrast, suggests that X is something I am actually interested in doing. However, in a conditional clause like this one, the difference between actual and hypothetical is quite small.

Edit: number 3 could possibly use a different meaning of should, that of obligation. In this case X is something I really ought to do, but instead of doing that I will do Y, something different. That's not really the meaning you are after, and might not be understood that way anyway, which is why I ignored it earlier.

In short, there is a fine distinction between the first example and the others, but for practical purposes you can treat them as the same.