You're interested in connecting two noun clauses, right? However, technically speaking, only Sentence 1 and Sentence 2 have two noun clauses. Sentence 3-7 each has only one noun clause (because there is only one の in each sentence). In other words, in Sentences 1 and 2, you are nominalizing two verbs independently first, getting two noun phrases, and then joining the two using と or や. On the other hand, in Sentences 3-7 you are first connecting two verbs using て, たり, etc., and then nominalizing it all at once using a single の. That's a large difference.
When you say "He likes to eat pasta and to drink beer," you are presenting the two actions more or less independently, right? Then the normal translation of this would be either Sentence 1 or Sentence 2. As for the difference between と and や, please see this: The many ways to say "and" in Japanese
Sentence 3 means he likes only one thing, "eating pasta and then drinking beer". Maybe eating pasta alone or drinking beer alone is not what he likes.
Sentence 4 is close to "He likes doing things like eating pasta and drinking beer."
Sentences 5-7 are grammatical but uncommon and nuanced. Basically they are similar to Sentence 3 in that he only likes one thing, but sounds more emphatic about the two actions happening simultaneously. These sentences imply ordinary people usually don't have pasta and beer at the same time, which I don't think is true.