UNID & unID, like Chanter says, mean unidentified station.
S3, S4 etc. is either a reading of signal strength from a radio's signal indicator (which can go from S1 to S9 and even S9+); or, in other cases (like mine) it's subjective, "S1" meaning you barely heard the programming, to "S5" meaning that it was pounding your earphones.
Other abbreviations you may encounter are 'hrd' (short for 'heard'), 'condx' (short for SW propagation conditions), QRM (interference from other stations), QRN (lightning, static crashes, atmospheric noises non-manmade), 'mx' (short for music -- used sometimes on AM band DX sites); 'CW' is morse code (usually heard on the ham bands). There are also abbreviations used for the various data modes you'll hear on the shortwaves in between the SW broadcast bands (FSK, RTTY, etc.).
As per usual, jargon sometimes can be a pain to deal with, but with SWLing and MW DXing, it's not really difficult -- mostly just abbreviations and a few ham radio Q codes.