I've used Purple Power and a pressure washer with good results. The pressure washer was from one of those do it yourself spray car washes. I took my jack and jack stands, raised the car, sprayed purple power, waited a bit, and then went to town with the spray washer. I also repeated the process.
Worked out great, but now it's kind of dirty under there. I'm about due for another bath.
BTW - Looks like there is remnants of grease from your left axle. Hopefully that was left from the previous axle and not the current. But we'll check it out.