You use "also" the same way you use "too" and "as well", only the placement in the sentence differs. Could you pass me the bread? And the butter also? (Also, the butter? And butter as well? And butter too?) Even can be used for the same purpose of adding but it adds emphasis, almost as a surprise that Leon mentioned. As if to say that it's not necessary but I'll do it regardless. If you buy the mattress, I'll even include the cover for free. Even is often used as a replacement fot something like "in spite of" I don't eat sweets but even I had that cake, it was so good.

The answer to your question depends on how the words are used. Both words have more than one meaning but are not at all synonymous with each other. Both of the examples J. Ríos gave, rely heavily on context (what would have already been said about the subject - the people at church) so would need preceding information to be fully understood. "The people at church (also) like the new songs" - The word "also" here indicates inclusion. Example: The people at church like old songs. They (also) like the new songs. "The people at church (even) like the new songs". The word "Even" used here adds emphasis and could indicate a sense of surprise or contempt. Example: The people at church like anything they listen to. They (even) like the new songs. Note the use of the personal pronoun 'they' which 'stands in' for "the people at church". Hope this helps.

They are both synonymous in this sense: The people at church also like the new songs The people at church even like the new songs but "even' can have other meanings as well.