led - MOSFET always slightly on and other strange behaviour

I'm trying to control my RGB LED strip with my arduino, using IRLZ34N MOSFETs according to this schematic

^{simulate this circuit – Schematic created using CircuitLab}

I tried it out, everything worked. I soldered it to a circuit board just like that, except for that I used 4 copper wires on the Arduino connections. Everything worked, I unplugged the copper wire from the Arduino and checked back ~3 Days later, then this happened:

The strip was slightly glowing, even when the gates of the MOSFETs are directly connected to ground. Connecting a Gate to +5v made that color glow fully though. That's pretty much my problem, some deeper examining got me those Results:

I desoldered the mosfets and my multimeter reads a resistance of ~290;310;350Ω between Drain and Source. Another strange behaviour is that the conduction seems to go from 0-100% really fast. My LED strip goes from the constant "slightly on"-State to 100% brightness in a matter of some mV. Also strange is that this happens at ~4.7V on the Gate, while my fully functional IRLZ34N gives the strip 0-100% brightness at around 1.5-2V.