Before I start...thank you everyone for responding. This makes my life a world of easier. In particular, Paul__B for your wealth of information and SirNickity for your flattery and effort.
Ok, it's pretty straightforward really.
As always, everything is straight forward when you have done it. 
The photodiodes are paralleled as you have determined and unlike the LEDs, they are not critically located to the reagent lines. In effect, you only have one photodiode surveying the whole strip.
There is a fair bit of engineering cleverness here. The fact that the LEDs are switched by the microprocessor means that they are only activated when you press the button (is it?) to read the result.
Yes, but they are initiated when someone pee's on the test. The pee forms a switch by shorting two conductors.
The whole device is pretty clever. The cost of production for the electronics is probably in the single-digital USD--~$3 is an educated guess. The only IC they use is a 8-bit microcontroller (similar to Atmel 8-bit AVR)--probably under $1-USD. The rest of the components are LEDs, Photodiodes, and SMD resistors & caps. The only other electronics are a battery and board. The fact that the microcontroller doesn't even use an analog input is pretty crafty. Intuition would suggest they use a analog input to detect light.
Obviously, they are switched on in turn (not in combination, so only a single current limit resistor is needed) to read each of the three lines and only for a brief time, so there is no wastage of battery power.
Sounds right…I got the Saleae Logic Analyzer and am going to confirm all this.
The device is obviously powered by a lithium coin cell.
Correct
The photodiodes are indeed a high impedance device, but then the microprocessor has very high impedance inputs, so should be able to read the current directly. We know that the Atmel processors discharge a (tiny) internal capacitor in the process of performing an analog reading - but you say these are only digital inputs. If the processor starts by switching the port to ground, then to an input and immediately begins to read the input, it will take a measurable time for the internal capacitance of the input and the photodiode itself to charge and for the port in this case, to go from low to high.
Sounds about right with my train of thought. Great to here my theory confirmed. (LIKE)
There is then no great complication in the arrangement - three lines to read (and I am not sure what the third is - there are generally two lines in such a strip test - the "test" and the "control" so I suspect there are here two "controls" on either side to confirm adequate wetting of the strip), three LEDs to illuminate them in turn with red light (since the blue of the reacted reagent is of course, "black" in red light) and two photodiodes working as one to monitor the readings. (Having two diodes actually increases the capacitance used to assess the photo-current by integration).
This makes a lot of sense why they are wired on the same net.
And I presume the interior of the casing is black or foil lined to exclude ambient light as you notice the PCB deliberately is.
(There is a black plastic fixture that is used to isolate the different LEDs/test lines with respect to the proper placement of the photodiodes. On top of that, it is in a white plastic shell that precludes light from entering as well. I have been using the fixture inside a cardboard box.)
I would be interested in other details of the device and display - whether it uses a button to "read" or is moisture-initiated (and times automatically from that, as I suspect it does).
(It is moisture initiated. The moisture shorts a junction initiating a test and turning the device on.)
I am not about to go out and buy one merely to dissect, and am not so fortunate as to have someone bring one in to my office and leave it with me (it usually works the other way around - they get to take the (non-digital) test home from me if the result is favourable, or at least positive and favourable as it canspuriously turn positive in time, something else that the logic here presumably prevents), so am not in a position to do the dissection for myself.
I know electronics is cheap and disposable, but this concept almost seems obscenely wasteful in a way.
Essentially, the board could probably do hundreds of tests even with a small coin cell battery that it has. However, for the purpose of simplicity they do not let you reuse the HW by letting you buy test strips separately. This could hypothetically even allow their margins to grow because the cost of production of test strips is probably VERY low (in the 10’s of cents for the quantities they produce). They could easily have a 100% mark-up. However, the ability to change out the test strip would complicate the design and would require instructions. Mind you, you are designing for your dumbest customer (anyone can design for the smartest because they can figure it out themselves). If you design products, you should design for your worse case, not the middle of the road or even worse—best case scenario.
If this is ‘wasteful’ is more a perspective than fact. A woman who gets pregnant not under the circumstances said person wanted to be pregnant under could definitely be a stressful time. Even a smart person, might not want to read instructions on what line means what. This gives a clear ‘Not Pregnant’ or ‘Pregnant’ answer. As a male, I don’t feel in a position to say if this is wasteful or not.
There are substances on used pregnancy testers known to the State of California to be icky.