Both words are used to describe intense or forcefully expressed emotions or opinions. Strong suggests felt or expressed with some degree of intensity: strong feelings; a strong objection, but strong’s wide range of application tends to dilute its precision and strength in these contexts. Vehement, which comes from a Latin word meaning “forceful” or “violent,” suggests something felt or expressed with intense passion. Vehement is not limited to a negative meaning (a vehement expression of his faith) but it does tend to be used most frequently for oppositional feelings and utterances: vehement protest, a vehement denial, vehement opposition.
Both words refer to a state in which all movement or progress has ceased. Standstill is used of both physical motion and more complex and abstract processes: The train came to a standstill; Negotiations are at a standstill. Impasse is a strong synonym for standstill in the latter usage: Peace talks have reached an impasse. However, it’s a more specific word, which suggests not only total lack of movement but also the impossibility of there being a way out or through. Standstill is often used of business, industry, the economy, and traffic, while an impasse is usually “between” two opposing parties and used of issues and discussions (the budget impasse; a political impasse). It’s common to speak of reaching an impasse, resolving or solving the impasse, or even breaking the impasse.
Both words refer to something that is readily apparent or easily perceived or sensed. As an adjective, clear has a wide range of reference: from materials (clear glass) to communication (a clear explanation). The relevant sense here describes something that is apparent, obvious, or easily perceived or understood: the team’s clear sense of pride. Palpable is a more emphatic, even dramatic word for something easily perceived, because of its literal meaning—able to be touched or felt—and its usual application to things like a mood, emotion, or atmosphere, which are insubstantial and can’t be touched. It suggests that an emotion or mood has such a strong presence that it is like something solid and material. The frequent use of the phrase almost palpable draws on both definitions of the word to make this point.