I don't know much about either the tubescreamer or the exp2, but since no one else is answering... maybe the output changes the tone of the pedal, probably not, but what it certainly will change is the signal level going into following devices. So the higher you set the output level, the more you'll cause the next device in the chain to overdrive or distort.
Between the guitar and hd500, if you want the dist first in the chain.
Otherwise, connect it between the fx send and fx return on the pod. You can place the fxloop anywhere in the pods chain, for example, guitar->hd500->noise gate->compressor->fx send/dist/fx return->amp. Leave the pedal always on, and engage the fxloop when you want it in your signal path.
You'll need to use the line6 link for this, which you should if you have a dt amp also. Using 4cm is sub-optimal as the fx loop on the pod is quite noisy and best avoided if possible.
A final option is to put things between the fx send and return on the amp, but this is mostly for reverb and delay although dist might work there too in some cases.