They are all past tense.
었다 = plain form. You hear/read it a lot when people are speaking 반말 (informally). Example: 먹었다? (have you eaten?)
었어 = conjugated form of 었다. Example: 먹었어? (have you eaten)
었지 = same thing as 었어 but the ~지 suffix has the nuance of the speaker assuming the verb has been done. Example: 먹었지? (you've eaten, right?)