Dear Sirs or Sirs "Mr. and Mr." appear to be plural. In that case the term is "Messrs." Otherwise you can say "Mr. X and Mr. Y."
The Honorable Judge Smith and Mr. Smith for the envelope and Judge Smith and Mr Smith for the letter.
What is the proper salutations for Dr. & Dr. Odie McKeaigg? If you are in Oklahoma, the proper way to address them is: "Hey punk (Odie) and Doctor Mckeaigg, How are you?"
Master
Mr. Mayor
Mr. Commissioner
Dr. and Mr. Smith.
Yes.
Mr President.
Dr. and Mr. Smith.
Dr. and Mrs. Smith
A proper salutation for greeting the president of a business is "Dear Mr. President". To conclude a letter, the proper word is "Sincerely" and a the name of the writer.
"Your Honor" or "Mr. (Mrs.) Mayor"