Guys, what sends the voltage to the injectors to fire? Does the crank sensor?
Crank sensor goes directly to the EZK ignition box. It tells the EZK how many RPMs the flywheel is spinning. LH Box senses LOAD via MAF and then shoots that information over to the EZK so it can compute proper ignition timing. EZK also talks to the LH box and tells it the RPM. When crank sensor goes out, you will not have spark OR fuel injector pulse. Modern cars dont have a computer for ignition and a computer for Fuel. It's just an old Bosch/Volvo thing.
The injectors always have 12v to the positive side of them with key on. The ECU GROUNDS the injectors for a matter of milliseconds to pulse them.
Black smoke usually means running rich. It can also be burning oil, but oil smoke is more of a white with blue tint. Sometimes it can be hard to tell them apart. It could mean bunk MAF (bunk MAF usually creates lean condition), bunk O2 sensor, bunk ECT sensor, excessive fuel pressure, leaking fuel injector or even leaking cold start injector (not common on Volvo for leaky injectors, but I guess it could happen. (Do a fuel pressure leak down test to determine if injector is leaking after shutdown.)
Use the multimeter to look at the 02 sensor at idle. It will oscillate between 0.1-0.9v once hot. If stuck at either extreme, bad. You can also remove it, put it on the bench, and hit it with burning propane and it will make voltage (NOT EVEN CONNECTED TO ANYTHING!) .9v=rich (when burning fuel is touched to it).
Repeat your diagnosis of the ECT sensor circuit. Also inspect the plug for it carefully. The pins can get pushed back into connector, corroded, or damaged. Unsheath the LH and EZK computer connectors and backprobe the pin for the ECT sensor and look at resistance readings with the connector unplugged.
I am sure finding somebody with a tailpipe gas analyzer will be difficult. Here in California, we have to get emissions testing and on older cars they shove an exhaust gas analyzer up the tailpipe and measure pollution levels. By analyzing the Hydrocarbon and Carbon Monoxide levels, it is possible to determine if the car is running rich or lean.
(the injectors) stay open a certain amount of time
The percentage that they are open vs. closed is percentage duty cycle. Time OPEN is pulsewidth. Duty cycle is a function of pulsewidth. Confusing. I know. It has taken me years to get to the level I am at.
Ever hear of Pulse Width Modulation (PWM)? The IAC on our car is PWM (aka) duty cycle controlled. So is the EGR vacuum solenoid. The computer sends PULSES to the component. Not a varying voltage. Modern cars use a lot more PWM controlled devices. The mechanical fan on modern Fords for example has a clutch that is controlled by the computer to be 0-100% duty cycle on/off. Modern cars also have PWM fuel pumps. It doesnt just get 12v all the time. It gets told how hard to work by the computer. Makes the pump last longer too. It's not going full blast like on our Volvos.
"What is duty cycle?" :
http://en-us.fluke.com/training/training-library/measurements/electricity/what-is-duty-cycle.html