All refer to making something visible which had previously not been visible
disclose = to make something known publicly that had previously been kept secret or hiddenShe signed an agreement not to disclose company trade secrets.
disseminate =

       divulge = to disclose or reveal information that would normally be kept secretGenerally speaking, a bank is not permitted to divulge information about its customers.
expose = to show publicly; to place on public view; to revealThe newspaper article exposed corruption in the country's two major political parties.
        The first one, disclose, usually is quite neutral and it refers to making public a factual matter. For instance, it is often said that "the seller failed to disclose hidden defects in the foundation of the house"
     We can also say that "she did not want to disclose the name of her lover".
     We often talk about the fact that "doctors are not supposed to disclose any information about their patients".
     In contrast, expose is not neutral but it usually implies some sort of scandal. So, for instance, we talk about "exposing corruption" or we talk about somebody who shows themselves, makes a part of themselves visible which is usually covered, for instance, "the paedophile exposed himself to children in the park". In this case he exposes his nakedness. We also talk about being exposed to liability and that means not covered or protected by some sort of a shield, for instance "a company was exposed to liability because it did not have any insurance coverage".

       The third word we have is divulge and divulge means making known very private, deeply sensitive information. We're revealing information which would normally be kept very secret. So, for instance, we talk about "divulging state secrets" for instance "an ambassador can be in trouble for divulging the state secrets that he has dealt with"
     or "police officers may not divulge the details of their undercover operations".
Now, two of these words have nouns that go with them, for instance, disclosure goes with disclose and exposure goes with expose. The word divulge has no noun. So we have to always construct our sentences to use a verb.
      For disclosure we would say, as we often do about contracts, "disclosure of confidential information is prohibited under the confidentiality clause of the contract"
      or for exposure we could say that  "she was prosecuted for indecent exposure because she appeared on the stage naked".

Outro termo relacionado: "leak"