1. Tom went camping with his friend John's family.

2. Tom went camping with John his friend's family.

3. Tom went camping with John's, his friend's family.

4. Tom went camping with John, his friend's family.

(Which one are grammatical?)

Only the first one comes close. Using the possessive form to try to express this type of thought will always result in ungrammatical or awkward sentences.

Try this instead:

Tom went camping with his friend John and family.

Out of the four options provided, option 1 is grammatically correct:

1. "Tom went camping with his friend John's family."

In this sentence, the possessive form "John's" correctly indicates that the family belongs to Tom's friend, John.

Let's analyze the other options to understand why they are not grammatically correct:

2. "Tom went camping with John his friend's family."
In this sentence, the possessive form is missing after "John." It should be "Tom went camping with John's, his friend's family" to indicate that the family belongs to Tom's friend, John. However, the repetition of "his friend's" is awkward and not necessary.

3. "Tom went camping with John's, his friend's family."
This option is similar to the previous one in terms of repetition. It attempts to combine both possessive forms, but it results in redundancy. It is better to stick with one possessive form, as in option 1.

4. "Tom went camping with John, his friend's family."
This option indicates that Tom went camping with John and also with his friend's family. However, it does not specifically state that John is Tom's friend. To clarify who John is, it is better to use the possessive form followed by the friend, as in option 1.

In summary, option 1 is the correct and grammatical sentence out of the four provided.