1. I liked the work very much because I could help orphans who needed love.

2. I liked the work very much because I could help children who had no father and mother.

3. I liked the work very much because I could help orphans who needed care.

4. I liked the work very much because I could help children who had no fathers and mothers.

5. I liked the work very much because I could help little childrens whose fahters they couldn't meet.

6. I liked the work very much because I could help orphans whose parents' were/are dead.

(Would you like to check the expressions above? Correct errors, please.)

The first four sentences are fine.

5. is confusing and not correct

6. No apostrophe after parents. Since orphan's parents are dead, you should end the sentence after "orphans."

Here are the corrected versions of the sentences:

1. I liked the work very much because I could help orphans who needed love.

2. I liked the work very much because I could help children who had no father or mother.

3. I liked the work very much because I could help orphans who needed care.

4. I liked the work very much because I could help children who had no parents.

5. I liked the work very much because I could help little children whose fathers they couldn't meet.

6. I liked the work very much because I could help orphans whose parents are/were dead.

Please note that the third sentence can also be written as "I liked the work very much because I could provide care to orphans who needed it." This is to ensure parallelism between the phrases "help orphans" and "provide care."