Which pedal should I put first, overdrive pedal or chorus pedal? Can they be on at same time ? I don't want to burn them out. I was wondering if an overdrive pedal would make a chorus pedal function better.
Pedal order is 100% personal preference, and there will be a difference with different placements. I would say it's more common to put overdrive before chorus but I've built pedalboards that have chorus in between two overdrives before. If they are both guitar pedals then you won't burn them out no matter how you place them in the signal chain. The main way you could damage a pedal electrically is by using the wrong power supply or battery.
As to whether one might make the other sound better, not exactly, but they can definitely sound awesome together.
There are no hard and fast rules with regards to the order of pedals in the signal chain, however, there are some general guidelines that may be of help.
Usually, a multi-fx signal chain will go something like this:
Wah -> OD/distortion -> EQ -> modulation FX (chorus/flanger/phasing etc.) -> delay -> reverb
So, if you were to subscribe to the "standard" set-up, you would put your chorus after your overdrive pedal.
Why this particular order? The general reasoning is to establish your general tone first and then successively colour it. Thus: the wah pedal acts almost like an additional, foot-controlled tone knob, following which overdrive determines the amount of distortion in your sound and the EQ shapes the overall tone. After you've established this base, you can further embelish it with modulation FX and if you wish to apply spatial effects - such as reverb or delay - these generally give the best results when they affect the entire sound.
In your particular case, a chorus effect will apply some measure of detuning to your sound by introducing an additional, slightly delayed signal. If you apply distortion (especially heavy distortion) to that, you might find that it becomes too noisy and dissonant. Conversely, if you apply the distortion beforehand, the two distorted signals will be separated and mixed within the chorus processor and offer a more "civilized" end effect.
Do bear in mind, that the above guidelines are just that: if you find the sound from a different order of effects more to your liking - go for it.
There should be no danger to the circuitry of the effects units from placing them in any particular order, but bear in mind that effects that boost the signal level (most notably OD/distortion, but compressors and EQ may also fall in this category) may overdrive the circutry in further effects down the signal chain, making the overall signal more distorted than planned. Every effect will also introduce some noise into the signal, which will be amplified by any signal-boosting effects further down the line, possibly becoming quite prominent. This is another reason to put such effects early in the signal chain and possibly put a noise gate between them and the rest of your effects.