-고 here is just the ordinary 'and' connector, and 들다 is one of the most overloaded verbs in Korean, so these lines do not share one meaning. Four of them are the compound 파고들다 'dig into, burrow in', literally and figuratively: 파고드는 시큼한 향 'a sour smell that digs into you', 내가 파고 들고 있기 때문입니다 'because I'm digging into it'. The rest are different verbs that happen to be spelled the same — 들고 다니다 'carry around', 들어보다 'listen', and the honorific 드시다 'eat'. Take the meaning from the whole compound, not from this pairing.
The examples below did not fully pin this one down — read them before relying on the entry above.