I have a VT30 and a VT20+ and neither has any trouble with my complete effects chain (using Tweed 4x10 on the VT30 or US Blues green light on the VT20+, Manual Mode, Bypass Mode), which consists of a Behringer Slow Motion, a Nobels ODR-1, Boss V-Wah, Boss BE-5 (4 pedals in one box - compression, OD, delay and chorus), BBE Boosta Grande all into the front end - no loop. I also have another chorus and a phaser pedal which I have added in without problem.
The only time I've ever had an issue like this was when I tried an Ibanez Weeping Demon Wah. It was overloading the front end of the Valvetronix and I had to turn the Gain control on the amp way down to get a clean sound. I therefore did not buy it.
jimstarla, is this problem present only when all pedals are on, all pedals off, or only some combinations? It may be just one pedal that's screwing things up. What happens when you reduce the Gain on the Vox? Try setting the level controls on all the pedals to unity gain, meaning the volume is the same with the effect on or off.
And yes, you should check all the patch cables.
And make sure all presets and effects on the amp are off.