1. I like him because of his honesty.
2. I like him on account of his honesty.
3. I like him on the ground of his honesty.
4. I like him thanks to his honesty.
5. I like him owing to his honesty.
6. I like him due to his honesty.
(Are they all grammatical? Do they have the same meaning? Do you have some more common expressions similiar to 'because of'?)
1-5 are correct, but 3 is not common at all. All mean the same thing.
6 includes an incorrect use of the word "due."
http://grammar.ccc.commnet.edu/grammar/plague.htm
See #7.
Yes, all the sentences you provided are grammatically correct. They all convey the same meaning, which is that the reason for liking someone is their honesty.
In addition to the expressions you mentioned, there are some more common alternatives to "because of" that you can use to convey a similar meaning:
1. I like him due to his honesty. (as you mentioned)
2. I like him as a result of his honesty.
3. I like him on the basis of his honesty.
4. I like him by reason of his honesty.
5. I like him through his honesty.
6. I like him given his honesty.
These expressions all indicate that the reason for liking someone or something is a specific quality or attribute.