I'm trying to achieve an output that would influence a multiplexer input
(74HC251). using the attached circuit, but I am unable to do so.

The LED1 is actually a photo-diode and the specs are located here:

http://futurlec.com/LED/INFD5940.shtml

My circuit has about 8 of them connected in parallel with anodes connected to each other and cathodes connected to each other.

What I used for R2 is 1 megaohm and for R1, I used 4.7 megaohm. Supply voltage comes from a 7805 voltage regulator with a 22uF decoupling capacitor. The source to the 7805 is a 9V battery.

I did some measurements with the voltmeter and with the battery at 6V, VCC of the opamp (also VCC to the resistor) is about 4V.

I then connected the meter between opamp pin 2 and ground and I applied a bright lazer beam onto the photodiode literally touching it, and the voltage changed by less than 0.5V.

I checked the output pin of the opamp as well and the results were still unsatisfactory.

The output I would ideally expect at pin 1 are two voltages depending on if light hits the photo-diode: sufficient voltage to produce a logic 1 to the input of the multiplexer (74HC251), or low voltage so logic 0 is produced.

I then proceeded to measure all the photodiodes together in parallel with the voltmeter using the ohms and then diode setting. With the ohms setting the meter didn't report anything, however when I set it to the diode setting and connected the meter anode to the diode cathode, and the diode anode to the meter cathode, I saw a 3-digit number on the meter that changed once a second for the first few seconds. When I reversed connection polarity, I got no reading.


Before assembling this whole thing on a breadboard like I did now, I used an unregulated VCC of 9V (instead of a max of 5V here) and I hooked an LED to the output with a resistor and when I passed the same light onto the photo-diode, the led changed from dim to bright, etc, responding to the light.

I begin to think my answer lies within changing part values to adapt to the 5V supply, but what values should I use?

 

You're using the wrong op amp to start with, and the wrong input method,
Try a 1Meg for starters and increase or decrease...

 

In your case, that of using a single supply, you can connect the + input of the opamp in Dodgydave's schematic to the output of a voltage divider that gives you 50% of the supply voltage, add a bypass capacitor to ground. This also provides some revers bias for your diode which should speed it up and reduce noise out of the tansimpedance amplifier.

 

Here's another option from a Nat Semi linear applications databook:

 

The circuit if Fig #1 is weird on so many levels.

I did some extensive I-V converter designs, namely the ability to bias +-10 V, 2 and 4 terminal, 4 ranges from 0.1 mA to 100 mA FS at 1V out full scale V(open circuit) was an option. The zero check and correct functions did not work. Since it was for in-house use, and it didn;t matter, I was not allowed time to fix it. The problem was identified as the D/A for zero had too high of a range and it did not output exactly zero volts.
Since I planned electronic zeroing, no offset provisions were designed in.

4 terminal compensates for lead resistance at low voltages and I even included +-50 mA of suppression if the bias was restricted to +-5V.

With no nulling provided, the amp had 40 pA of offset which was fine. I cared about he AC performance which was excellent.

With the addition of a few parts you can amplify just the offset voltage.

That said, the most important parameter is Vos. With many diodes in parallel you MIGHT have problems with capacitive loading.
That was another issue that came up very early.

Watch: Most IC converter designs use dual supplies and output a negative output.

 

See