Current in a single terminal voltage source?
I know there can't be voltage without current...


You can have voltage without current. Just have a battery, not driving anything


  ...  but how can I calculate the current in a wire if I only have the voltage and there is supposed to be no resistance?


An ideal wire (what simulators assume) has no resistance. So you compute the current through it by adding up the current in the components connected to it.

So in your diagram, the red wire to -15v is fed by that diode.

Let's assume the diode is dropping 0.7v, a convenient approximation that is useful at this stage of the solution. That puts the voltage at the junction of the 2.2k and 1.5k resistors at 14.3v (wouldn't it be much easier if those components had reference designators, so I could say D1, R2, R3?)

Now we know the voltage across the 1.5k is 15v-(-14.3v) and that across the 2.2k is 14.3v-(-14.3v), so using Ohm's Law we can compute the current through both. This current flows through the diode, and flows through the wire to -15v.

In the same manner, you can calculate the current in the 1k resistor, which flows between +15v and ground, not to the -15v line.

Now you have a first approximation for the currents in the diodes, you could go back and refine the diode voltage drops a little, to recalculate the voltages and hence currents, if you wanted more accuracy.