On the other hand, it can give a kind of casualness to a sentence and so makes it sound less blunt: Ja ("you know"/"everyone knows"/"I already told you") indicates that the speaker thinks that the fact should already be known to the listener and intends the statement to be more of a reminder or conclusion: Doch can have several meanings.
However, at least in writing, schon "already" must be either made unmistakable by the context, such as by additional adverbs, or replaced by its equivalent, bereits: In other contexts, doch indicates that the action described in the sentence is unlikely to occur: Gar is used to intensify a statement, the completeness or a total lack of something: At the beginning of a sentence, especially in literary contexts, gar sometimes has a different meaning and is often interchangeable with sogar or ganz: Rein often precedes gar to point out the total lack of something: Total, besides its use as an adjective and adverb, can also act as a modal particle indicating irony.
It is best translated as "well", "really" or "let me think...": Aber, when not as a conjunction, is very similar to doch and conveys a meaning of disagreement to a previously stated or implied assertion.
Giving an adequate translation even into Standard German is difficult, and the best substitute would probably be to use an understatement with strong affirmative meaning.
In English, translations to "I should think" or "just to mention" seem possible depending on context: Wohl is often used instead of epistemic adverbs, such as vermutlich or wahrscheinlich or to emphasise a strong disagreement.