I had someone tell me to connect the tape deck through the aux, but I'm not sure if I should plug them in through the aux return or send. Would anybody happen to have any advice?

You should be able to get enough juice from the 320 to roast your tape deck.

First, decide what you want to be Tape Out. This could be (in descending order of likely utility):

Master L-R (XLR out)
Master B L-R (TRS out?)
Groups 1 and 2 (TRS out)
Groups 3 and 4 (TRS out)
Monitor Out (TRS out. Watch out for Solo!)

and then various aux outputs which are all likely to be even more complex because it's sometimes confusing to set the aux sends correctly. I'm not going to deal with those here.

Now, you probably have something going to the local PA system...likely Master L, R, or both (the speaker setups in many churches are mono, not stereo--don't know about yours). Or perhaps you are using Master B. The nice thing about the Venice is that you have both, and you can set the levels independently. If you send one to your PA and the other to your tape deck and you find you are getting some, but not enough signal to the tape deck, swap the two and see how things go. What should happen is that if you were really dialed down on the Master before, you'll dial up after the swap, and you can compesate with Master B.

If you want fader control instead of knob control, you can allocate a group or a pair of groups (depending on whether your signal is mono or stereo) and then just be sure to always engage the appropriate group buttons every time you engage the L-R buttons. Then feed the deck from the appropriate groups.

You can download the Venice manual from the midas website (http://midasconsoles.com) from the support->downloads section.

First thing is that you probably have the gain structure messed up. It happens in Churches where volume could be massive, but is for most of the time quieter.

When the mixer is being used, how far up do the output faders meters go? I bet that for much of the time they are not even remotely half way up. Your amplifiers are probably just turned up to make the volume in the room 'correct'. This is not how it should be. You should be operating the mixer so that the levels are using the full dynamic range of the mixer, then adjusting the gain on the amps so the room volume is right.  Your tape outputs will then be much hotter. 

The Mixer you have is old, but very good. It's also very quiet, so the gain staging you've got wrong, doesn't show up as a noisy output.

You should connect each sound source, then use the mixer's meters to set the channel gain - then with it's fader around unity, raise the master until you have headroom at the top for peaks, but not too much. Then slowly raise the amp gains until the room sound is correct.

If you then add lots more channels set the same way, you then either lower all the channel faders, or you could drop the master - so the master meters stay around the same maximum level. Some people do a bit of both. If the master output is now much hotter - so will the tape output, so you do the same level adjustment. Depending on your system - you pick the maximum. Remembering that digital absolute maximum is an level never to be exceeded, your analogue desk goes over the 0dB point and can have even hotter output. It's difficult to get it right!