The answer to your questions are unfortunately not trivial. Especially in the case of PCBs as traces will dissipate heat into the PCB and it will be cooled by convection. You must also decide what is a “safe” temperature to operate at. Many other factors contribute to estimating the correct trace size for a specific current.
Regarding the spacing of your external traces the standards say (for 110V) that PCBs with no solder mask should be spaced 0.6mm apart, with solder mask 0.4mm. That is assuming your application altitude is less than 10,000 feet. Having said that more space is always better!
The question of how wide to make traces to handle a specific current load is not trivial. This will depend on the thickness of your copper on the PCB and the temperature rise you can accept.
Assumptions:
External Traces
PCB Substrate is greater than 0.8mm thick
Copper Thickness is less than 108um
Temperature rise from ambient @ STP
Here is the temperature rise for specific cross sectional area for 20 A:
1 oz copper (1.4 mils)
100 C 250 Sq. Mils
75 C 300 Sq. Mils
60 C 350 Sq. Mils
45 C 400 Sq. Mils
30 C 500 Sq. Mils
20 C ~700 Sq. Mils
So for a reasonable temperature rise (30 C) you can calculate the size of the trace. Add a 10% derating to account for copper thickness, conductor width estimates, and cross-sectional area.
1 oz copper (1.4 mils) - 360 mils + 10% = ~400 mils
2oz copper (2.8 mils) - 180 mils + 10% = ~ 200 mils.
Regarding the Stranded wire gauge. You will have to calculate the equivalent cross sectional area. The size of a stranded wire is defined in the following way: 18AWG 16/30. The overall diameter of the wire is AWG 12 (2.05mm) and it is made up of 41 strands of AWG 30. AWG 30 has a 10 mil diameter so the cross sectional area is 0.05mm. Multiply that times 41 and we have our equivalent cross sectional area 2.05 mm^2 . That is about the same size as 14 AWG (2.08 mm^2) solid wire. (I know it looks strange because of the relationship of the cross sectional area to diameter of 14 and 12 gauge).
Now that you have your equivalent wire size, you must once again consider the temperature rise. Checking the National Electric Code will tell you that for a wire with insulation rated to 90 C you can run 14 amps through the stranded 12 gauge wire (solid 18 gauge). The NFPA (they write the NEC) has determined what they deem safe. You can find all the info on current carrying capacity for solid copper wire on wikipedia.
http://en.wikipedia.org/wiki/American_wire_gauge
For long runs you will also have to consider the distance you will run your wire. 14 Gauge copper has a resistance of 2.525 mili Ohms per foot. The longer your run the wire the less power you can deliver.
Keep in mind this only holds for copper wire. Aluminium wire for instance would have a different diameter for a given AWG. AWG is the resistance per unit length in decibels. AWG = 10 x log10(R) + 10.
Hope that helps.