These fixed phrases paint a picture instead of saying things plainly, and all three are informal/spoken — natural in chat or a casual email, but keep them out of formal writing. The last straw (negative) is the final small problem that finally makes you give up; under the weather (neutral, mildly negative) means feeling a bit unwell; a piece of cake (positive) means very easy. You cannot swap the words: it is never 'the last stick' or 'a piece of pie'.
Idioms for feelings and difficulty
the last straw /ðə ˈlæst ˈstrɔ/ — Missing the deadline was bad, but her rude email was the last straw.
under the weather /ˈʌndər ðə ˈwɛðər/ — I'm feeling a bit under the weather, so I'll skip the run today.
a piece of cake /ə ˈpis əv ˈkeɪk/ — After all that practice, the driving test was a piece of cake.
Not ""Her criticism was the last stick that broke the camel's back." (wrong word)" — say ""Her criticism was the last straw." (fixed idiom)". The idiom is the last straw, not 'the last stick'. Keep it short, the longer form is the straw that broke the camel's back, so don't blend the two into 'the last straw that broke the camel's back'.
Try it: Choose the correct form of the idiom that means 'very easy'. (The presentation was a piece of cake. / The presentation was a piece of pie. / The presentation was a cake piece.) Answer: The presentation was a piece of cake. — 'A piece of cake' is the fixed idiom for something very easy. 'A piece of pie' swaps in the wrong noun, and 'a cake piece' reorders the words, which idioms never allow.
Idioms for problems and agreement
More vivid fixed phrases, and again all informal/spoken, great for conversation, but swap them for plain wording in a formal report. Open a can of worms (negative) means to start something that creates lots of new problems; the tip of the iceberg (negative) is the small visible part of a much bigger issue; on the same page (positive, common at work) means everyone shares the same understanding. Watch the plural in walk on eggshells (negative), to be very careful around someone so you don't upset them, never 'walk on eggs'. Two of these quietly criticise someone: open a can of worms blames whoever raised the topic, and walk on eggshells says the person you tiptoe around is difficult, so don't say either to their face.
open a can of worms /ˈoʊpən ə ˈkæn əv ˈwɜrmz/ — Asking about the budget really opened a can of worms in that meeting.
the tip of the iceberg /ðə ˈtɪp əv ði ˈaɪsbɜrɡ/ — These complaints are just the tip of the iceberg; the real problem is much bigger.
on the same page /ɑn ðə ˈseɪm ˈpeɪdʒ/ — Let's have a quick call so we're all on the same page before we start.
walk on eggshells /ˈwɔk ɑn ˈɛɡʃɛlz/ — Everyone walks on eggshells around him after a bad review.
Not ""In this formal report, the findings are just the tip of the iceberg." (informal idiom in formal writing)" — say ""In this report, the findings point to a much larger underlying problem." (plain wording for formal writing)". These idioms are informal/spoken. In casual talk they add colour, but in a formal report or essay, swap them for plain language.
Try it: Which sentence uses the fixed idiom correctly to mean 'be very careful around someone'? (We have to walk on eggshells around the boss. / We have to walk on eggs around the boss. / We have to walk on the eggshell around the boss.) Answer: We have to walk on eggshells around the boss. — The idiom is 'walk on eggshells', with the fixed plural. 'Walk on eggs' changes the noun, and 'walk on the eggshell' both adds 'the' and drops the plural; idioms don't allow either change.
Try it: Someone says a reported issue is only a tiny part of a much larger problem. Which idiom fits? (the tip of the iceberg / a piece of cake / under the weather) Answer: the tip of the iceberg — 'The tip of the iceberg' is the small visible part of a far bigger problem, which matches exactly. 'A piece of cake' means easy, and 'under the weather' means unwell; neither is about the scale of a problem.