This is probably not your issue - but it would definitely help if you got a modern multimeter - It seems that you're pretty new to putting circuits together, so having to factor in the loading of a moving-coil voltmeter into your measurements may not be helping you so much...
On to your circuit - can you draw a diagram of what you've got? It's reasonably difficult to pick out what you're doing from your picture - but I'm pretty sure you've wired it up wrong The circuit should be like the diagram below. Note well that the pinout of the LM317 does not match the drawn pinout arrangement on the schematic diagram.
View attachment 63794
Another thing - when you get it working, I'd want to rebuild your circuit on a prototyping PCB before you connect it to a diode - Laser diodes may not tolerate the harsh transient changes that an insecure connection will cause - Good solid soldered joints are really the easiest
reliable connection to make here.