SODA: For static defects, a one time demonstration that the defect does not impair your ability to perform flying functions in the real world. Essentially a waiver based on the fact that a real-world test is a better evaluation of individuals than regulatory standards.
Waiver: For static defects, the FAA determines that while you don't meet the certification standards (and either cannot or have not passed a SODA) that the defect in question is of minimal impact on overall aviation safety.
Special Issuance: Like a waiver, but for conditions which are likely to change within the renewal interval for the medical class in question. This normally means that the medical is not valid for the normal length of time, or typical in the case of a 1C SI, that it is not good for ANY class of medical after six months.
The SI time interval is actually annotated on the medical, so a potential employer would see that. I don't think SODA's or waivers are noted on the medical certificate itself, they are a separate document which you retain which authorizes the AME to grant you a normal medical in spite of the defect.