If and unless are common conditional conjunctions employed to express conjecture and uncertainty, but a number of other words and phrases that perform similar functions are discussed in this post.
“Should you” is the future conditional form of “do you,” seen in formally polite requests such as “Should you have any questions, please do not hesitate to contact me.” It is more flexible than “if you,” which is strictly conditional in the present, in inviting the audience to contact the speaker/writer at any time, not just now.
“Had you” is an example of a subject-auxiliary inversion, employed in statements such as ‘Had you bothered to ask, I would have told you.” The implication of the sentence is that the audience did not do something that, if he or she or they had, would have achieved the stated result.
“If (noun/pronoun) were” statements pertain to possible but improbable occurrences or to recommendations, as in “If you were to open your eyes, you would find what you were looking for.” A more formal version of this form is “were (noun/pronoun) to (verb),” as in “Were we to think otherwise.”
Several words or phrases impose conditions or set limits, such as “As long as” (less formal) or “so long as,” (more formal), “only if,” “on condition that,” and “provided” or “providing” (or “provided/providing that”).
The conjunction or is used conditionally to establish an alternative possibility to a condition or state: “Hurry up, or you’ll be late.” Otherwise, as used earlier in this post, is a pronoun; as a conjunctive adverb, it serves the same function as or (but notice the difference in punctuation): “Hurry up; otherwise, you’ll be late.” (Some writing guides accept the punctuation used with or.)
Suppose and supposing apply to what-if situations: “Suppose that I were to say no—what would you do?” “Supposing that I were to say no, what would you do?” Suppose also pertains to proposing an idea, as in “Suppose I pay for dinner, and you buy the movie tickets?”
In “if only,” only appears as an intensifier to express a strong wish for a different condition or state, as in “If only you had told me before.” “If so” and “if not” pertain to opposite potential affirmative and negative conditions or states, respectively, when the condition or state is known: “Do you plan to attend the event? If so, click on yes. If not, click on no.” Even is also used as an intensifier with if, but unlike in the case of only, it precedes if; it pertains to extreme or surprising conditions or states, as in “Even if I were to believe you, what would you expect me to do about it?”