Right-click the layer you would like to create multicolor/multi-line, choose Properties… and go to the Labels tab, and click the “Expression…” button.
For example, to have the New ID on top and the Old ID on the bottom:
To have each a different color:
“<CLR Red=’255′>” & [New_ID] & “</CLR>” &vbnewline&”<CLR blue=’255′>”&[Old_ID]&”</CLR>”
The tricky part was figuring out that you had to put double quotes around the formatted text, and drop the normal double quote down to a single quote around the 255.