Does this clearance allow me to fly a reciprocal of 020 inbound to the station? Or will I just have to fly away from the station on 020 radial?
A radial is always pointing away (radiating) from the VOR. The clearance therefore instructs you to fly away from the VOR on the 020 radial.
Will a left turn be more appropriate than a right turn to intercept radial 020?
I think the image should answer that: right turn is better.
In a Cessna 172, I would twist the OBS to get a from flag and then select 020, how do I ago about this in a 737 sim? Is it the same thing?
You can tune the VOR frequency on the ground using the NAV tuning panel on the center pedestal (left image) and then dial in the course of 020 on the Mode Control Panel (MCP) on the glareshield (right image):
(737 NG FCOM)
Do I select the radial before or after take off?
You can do it before takeoff because you will depart using runway heading (in HDG SEL mode) initially.
Finally, the b737 uses ADI with a movable pointer or "sky up"which is different from what single pistons and light twins use. I will appreciate any tips to help me nail the movable pointer ADI/attitude indicator on the sim.
You depart in HDG SEL (8 in image below) with a heading of 300 (or runway heading) until 2000ft and then turn right onto a 065 heading (still in HDG SEL). This will set you up for a 45° intercept of the radial. Note: With strong winds, you need to correct this heading to get a 065 track.
To arm the intercept, you select the VOR LOC mode on the MCP (5 in the following image):
(737 NG FCOM)
This will arm the VOR intercept (should show VOR LOC as an armed mode on the FMA (Flight Mode Annunciator), which is located at the top of the Primary Flight Display). Now all you have to do is follow the flight director (or turn on the autopilot and watch it do all the work).
If you don't want to use the flight director, you can switch the Navigation Display (ND) to VOR mode on the EFIS (Electronic Flight Instrument System) on the glareshield (2 in the following image, when turning 1 to VOR you also get an ADF like pointer towards the VOR):
(737 NG FCOM)
The ND will then look something like this:
(737 NG FCOM)
Here, you find familiar things like lateral deviation (10), TO/FROM indicator (12, also shown as arrow inside) and the selected course (3). It is using heading up or track up, but it works exactly like in a C172. The easiest way to fly the intercept is however to use the flight directors.