Here's some information about them, Eric48.
By General Order No. 111, dated March 18, 1864, the title Veteran Reserve Corps was substituted for that of Invalid Corps, and this title is used in almost every case in the present work, whether the reference is to transfers and enlistments prior to March 18, 1864, or to those made subsequent to that date.
The men serving in the Veteran Reserve Corps were organized into two battalions, the First Battalion including those whose disabilities were comparatively slight and who were still able to handle a musket and do some marching, also to perform guard or provost duty; the Second Battalion being made up of men whose disabilities were more serious, who had perhaps lost limbs or suffered some other grave injury. These latter were commonly employed as cooks, orderlies, nurses, or guards in public buildings. There were from first to last from two to three times as many men in the First Battalion as in the Second, and the soldiers in the First Battalion performed a wide variety of duties. They furnished guards for the Confederate prison camps at Johnson's Island, Ohio, Elmira, N. Y., Point Lookout, Md., and elsewhere. They furnished details to the provost marshals to arrest bounty jumpers and to enforce the draft. They escorted substitutes, recruits, and prisoners to and from the front. They guarded railroads, did patrol duty in Washington City, and even manned the defenses of the city during Early's raid in July, 1864.
An excellent sketch of the history of the Veteran Reserve Corps may be found in Volume V, Series III, of the Official Records of the Union and Confederate Armies, pages 543 to 568.
There were first and last twenty-four regiments in the Corps. In the beginning each regiment was made up of six companies of the First Battalion and four of the Second Battalion, but in the latter part of the war this method of organization was not strictly adhered to. The 18th Regiment, for example, which rendered exceptionally good service at Belle Plain, Port Royal, and White House Landing, Va., in the spring and early summer of 1864, and in or near Washington City in the latter part of the summer and through the fall of that year, was made up of only six Second Battalion companies.
http://www.civilwardata.com/vrc_desc.html