For high currents and thick wires, a gas-tight crimped junction is the industry standard choice.
While solder appears to have its advantages, the key issue to keep in mind is the challenge of soldering 1 AWG copper wire, where the thermal conductivity of the wire itself will rapidly draw heat away from the soldering location, and insulation etc elsewhere on the wire would get overheated and damaged. Of course, for such uses, a blow-torch type gas soldering gun would be used instead of conventional soldering irons, but the issue remains.
Another concern with soldering is that the solder itself could potentially melt and run, leading to an all round mess, if the junction were to heat up enough, a distinct possibility at 160 Amperes.
Screw terminals would work, but the risk is of the terminal tabs coming loose over time due to mechanical vibration, and also of oxide formation at the metal contact surface, leading to increased resistance, thereby heat, and another all-round mess.
A crimped spade terminal actually creates a metal-metal colloidal bond at the surface between the wire and the terminal, and if done right, no gas remains between the surfaces. This ensures longevity and safety, making this the preferred mechanism in industrial implementations.
The only real limitations are how much power you can pull from your supply and how quickly the electromagnet heats up (remember it's a glorified heater as well as a magnet). The strength of the magnet is dependent on both the number of turns and the current (Ampere-turns). 1 turn at 10A has roughly the same magnetic strength as 10 turns at 1A. The difference is more turns means more resistance which will try and limit the current so you then need more voltage to push more current through the coil. If you've got lots of wire try a few combinations (be a good demo to have two magnets which lift the same weights yet have visibly different numbers of turns, a 9V battery powering a high turn count, low current magnet and some AAs in parallel powering a low turn count, high current magnet - that'd really confuse your audience)
Best Answer
Is this for a high temp situation where solder might melt? What was suboptimal for your crimp? Reliability?
You could spot weld them like a thermocouple. http://www.sunstonespotwelders.com/spot-welder-200ws-single-pulse.php might handle wires that small. Another options might be simple screw terminals.