Strange behavior on diy OR logic gate
Zooming in your photo, i can see that there is flux on the board. Have you washed your board after soldering? If there is flux left on it, it acts as a conductor (sometimes). It has to be clean. Clean it using isopropanol (if you dnt have isoropanol you can use alcohol but if its not 100% clean alcohol it can corrode your leads)
Other that that, your circuit looks fine, but you may reduce the resistance of your 10k resistors to allow more current through the transistor for your led to switch fully on. Also you can add a pull-down resistor on the gate of your transistor to reduce the capacitive noise created by you, when you get close to your circuit (make sure to use a bigger value resistor for your pull down than your 10k resistors so that more current flows in your transistor rather than ground.