[Byrne]

Okay, so if the critical point of oxygen occurs at a temperature of 154.58 K and a pressure of 5043 kPa, does this mean that if the temperature of 154.58 is increased to, say, 156 K it is impossible to liquefy oxygen, even if the pressure is increased by tens, hundreds, thousands, etc of units?

[plu]

Yep.  Check out a phase diagram of oxygen to confirm.