Hi,
I don't see any inconsistencies, but you have to be careful about the actual Vds/Id values present at the same time.
First of all, Note A in the attached data sheet says that the absolute maximum ratings are based on the thermal resistance rating for t<=10s, which is at max 40°C/W. I admit that it is odd to specify the maximum continuous current via this transient thermal resistance, but I assume they have valid reasons for that. Maybe someone else has more insight and can provide an explanation.
1) When the MOSFET is fully on, its Rds is around 6mOhm. Given Id=18A the total power dissipation is around 2W. Compare this to the asymptotic value of the Power rating curve and you will find that their the same. Furthermore, given the Rth=40°C/W, the junction is P*Rth=80°C warmer than the ambient temperature (25°C), so the junction is at roughly 105°C. Hence, in order to stay below a certain junction temperature (in this case around 105°C) the current must not exceed 18A at Ta=25°C, which is why the manufacturer specifies this current as the absolute maximum rating.
At the same time, Rds=6mOhm results in a Vds =Id*Rds= 0.11V, which is exactly what you can see in the SOA graph. So no inconsistencies there.
2) When switching a load via a MOSFET, Vds=Vsupply when the FET is off, and Vds is approximately zero when the FET is on. Keep in mind that you want the voltage to drop across your load and not across your FET. Thus, the 19V / 5A are never present at the same time. (If they were, your FET would dissipate around 100W and your SOP8 case will probably explode within a second). Thus, in the off-state you have Vds=19V Id=0A, and in the on-state roughly Vds=0.1V Id=5A, that's why the MOSFET doesn't blow up.
And, to answer your final question: The SOA tells you exactly what its name implies: The maximum safe Vds/Id combinations for different pulse-lengths. The Vds in this case is the actual voltage in the on-state. Therefore, if you really have Vds>15V in the on-state, the maximum safe Id is below 100mA.
I hope this helps in resolving your confusion.