Where is the distance of a race track measured inside stripe or outside stripe

Do not know about other sports but in Speedway the length of the track is measured on a line 1 metre out from the inside kerb.

That really depends upon what is racing on the track. In NASCAR (not my favorite), the track is measured from a point 15 feet in from the wall, going around in a circle.
(ref :http://nascar.about.com/od/nextelcuptracks/tp/longesttracks.htm)
whereas on some road courses (with multiple left & right turns & chicanes) the ''race line'' is measured with a fifth wheel (this is usually considered the centre of the track as an average). The FIA states:
The length of a circuit for the calculation of race distances, race records & classifications is considered to be that of the centreline of the track.Unless otherwise stated, all references to straights & curves in these criteria concern the actual trajectory followed by the cars with the highest performance & not the geometrical form of the layout (The trajectory, when traced on the plan, will generally have the effect of reducing the straights & elongating the curves: when planning or modifying a course, the designer must base his calculations upon it).
fia.com/resources/documents/108211263__Appendix_O_a.pdf