[noun] + がする [noun] + の + [noun] + がする [i-adj] + [noun] + がする
がする says that a smell, sound, taste or feeling reaches you. The sensation is the subject and takes が; the person who notices it is usually left out. The noun before がする is a sense word: におい匂い, おと音, こえ声, あじ味, かんじ感じ, き気, よかん予感.
The sensation takes が, not を.
がする is for what comes to you whether you try or not. To listen on purpose use きく聞く, and to sniff on purpose use かぐ; both take を.
Some symptoms take がする too: かんき寒気 (chills), はきけ吐き気 (nausea), めまい (dizziness), ずつう頭痛 (a headache).
These go beyond the plain sense nouns.
With なん何の and も, the negative means "no taste, no smell at all".
After a plain-form clause, きがする気がする means "I have a feeling that…". It is a separate grammar point.