ajn22anellie,
The residual strain in your welded assembly is due to localized thermal expansion/contraction while the weld joint itself, plus other portions of the structural weld joint not yet fully fused (ie. still tacked), are plastically or elastically displaced.
The least costly remedies (as others have noted) is to employ pre and post heating. You should also work out a process for welding each part of the joint in a specific order, since balancing the heat inputs to the structure will help to minimize thermal strains.
Finally, yes there is such a thing as a vibratory stress relief process. It is generally employed on weldments that are too large to thermally stress relieve. However, personally I've only seen it used with large welded aluminum fixtures, that needed post weld machining. Aluminum weldments tend to have lots of residual strain, probably due to aluminum's high thermal conductivity and the higher amounts of heat input required to fusion weld it. You are using A36 mild steel, which welds beautifully and probably results in a welded structure with the least amount of weld distortion of any material I can think of.
For vibratory stress relief services, check Meta-Lax.
Good luck.