Otto, I checked my trusty copy of When The Steam Railroads Electrified by William D. Middleton last evening.
The dates you are looking for: N&W ended electrification in the summer of 1950 (no specific date given).
The Virginian portion of the N&W (N&W and Virginian merged at the end of 1959) ended electric operations on June 30, 1962.
A little more information: The N&W was electrified between Bluefield and Iaeger, WV in 1912, mainly to work the Elkhorn grade. The N&W power plant was in Bluestone, 11 miles west of Bluefield. The N&W upgraded the line with the lessening of grades and double tracking, opening the reroute in 1950, negating any further use of electrification on the N&W.
More information here: http://www.nwhs.org/about_nw.html
(Scroll down to Electrification.)
The Virginian portion was 134 miles long, electrified in 1923, running from Mullens, WV to Roanoke, VA. The VGN power plant was in Narrows, VA on the New River. As mentioned earlier the N&W and the VGN merged at the end of 1959, with the parallel lines making better use of ruling grades for loads headed to the tidewater ports, ending the need for the VGN electrified portion. Some of the newer electric locomotives were sold to the New Haven, eventually serving PennCentral and Conrail.
More information here: http://www.nwhs.org/about_vgn.html
Again, scroll down to Electrification.