These are mainly self-explanatory with the exception of cheese itself, which is of doubtful origin but may be from Persian and Urdu CHIZ meaning thing. As a phrase, big cheese seems to have originated in early 20th-century US slang, as did big noise. Big wheel in this metaphorical sense (as opposed to the fairground ride known as a Ferris wheel) and big shot are similarly US in origin (mid 20th century). Big fish may have connotations either of something it is desirable for you to catch or of the metaphorical expression a big fish in a small pond.
a big fish in a small pond = a big fish in a pond
a person seen as important and influential only within the limited scope of a small organization or group
drink like a fish
drink excessive amounts of alcohol, especially habitually
fish or cut bait
stop vacillating and decide to act on or disengage from something – North American informal
a fish out of water
a person who is in a completely unsuitable environment or situation
1991 - Margaret Weiss - King's Test - He realized that he was a fish out of water—a pilot in the midst of marines.
have other fish to fry = have bigger fish to fry
have other or more important matters to attend to.
1985 - Gregory Benford - Artifact - Kontos can throw a fit back there, chew the rug, anything - it won't matter. His government has bigger fish to fry.
like shooting fish in a barrel
done very easily
1992 - Laurie Colwin - Home Cooking - I fear that's the urgency of greed. Picking cultivated berries is like shooting fish in a barrel.
neither fish nor fowl = neither fish nor fowl nor good red herring
of indefinite character and difficult to identify or classify
This expression arose with reference to dietary laws formerly laid down by the Church during periods of fasting or abstinence.
a pretty kettle of fish = a fine kettle of fish
an awkward state of affairs – informal
In late 18th-century Scotland, a kettle of fish was a large saucepan of fish, typically freshly caught salmon, cooked at Scottish picnics and the term was also applied to the picnic itself. By the mid 18th century, the novelist Henry Fielding was using the phrase to mean a muddle.
there are plenty more fish in the sea
used to console someone whose romantic relationship has ended by pointing out that there are many other people with whom they may have a successful relationship in the future.
This expression alludes to the proverb there are as good fish in the sea as ever came out of it.