rear is a 27
i dont think it has changed over the years so matters not what year model yours is
That's wrong. The rear is a 24mm nut and always has been of that size on the DR650SE afaik. (Checked just now)
The other side of the rear axle has a 22mm hex but you don't really need it as the adjuster will prevent the axle from turning.
The front axle has a 19mm hex, no nut, screws into a thread in the left lower fork tube. The clamp nuts are 10mm.