There are some excellent and very technical discussions of this on the net, but simply as I understand it, it is difficult to determine exactly the point where the material transitions from a plastic to an elastic response (which would be the real yield point) (called the proportional limit) so they establish an arbitrary point that can be easily measured. That point is .2% of a pre-established gage length, usually 2". The .2% offset is the reported 'yield point' used on your MTR. Elongation most often is the total 'stretch' of the material at fracture, measured as a percentage of the original gage length (same one). You put the two fractured pieces back together again and measure how much the material is longer than its original length and then do the math.
If it is now 2 1/2" long you have 25% Elongation.

I don't know what materials or specifications you are dealing with but you should carefully read the spec footnotes and references.  It is not unusual to see that allowances are made for circumstances that seem to be out of spec but turn out not to be.

An example of this is CVN testing for A709 materials.  It would appear that all CVN specimens should meet the minimum impact values, However if you chase through the references, you'll see that 1 specimen can be less the minimum, as long as it is at least 2/3 of minimum and the 3 specimen average meets minimum or higher.

Some of those might be there in a way that doesn't jump out atcha.

I'm not sure about "OFFSET" but I'll bet if you look in ASTM A370 you might find out.  (Sorry - none handy to me at the moment)