Commonly, you arrange the pedals in a way that the guitar signal first passes the overdrive pedal and is then send to modulation effects like delays or reverb pedals.
But in my honest opinion, it is worth it to change this accustomed layout.
Overdrive before the delay
By using the overdrive pedal BEFORE the delay and the reverb pedal, the guitar signal becomes overdriven before it is repeated by a delay or reverb pedal.
The overdriven signal maintains its own sound and will only be modulated by the character of the delay pedal.
Overdrive after the delay
However, to place the overdrive pedal AFTER the delay can also offer some advantages.
By passing the delay first, the initial repeats of the signal will louder than the following.
When this signal runs through the subsequent overdrive pedal, the level of distortion will also decrease gradually.
By adjusting the overdrive pedal in a way that the sound will be overdriven very gently, it is possible to change between slightly overdriven and clean sounds.
The tone pot or tone stack which most overdrive pedals offer, can be used to form the signal of the delay.
From experience, analog delays interact better with overdrive pedals than digital delays do.
To create a nice melting of the sound of a digital delay with the guitar signal, you can turn the tone pot into almost full counterclockwise direction.
To me, it seems that an overdrive pedal AFTER the delays produces a more pleasing signal that merges in miraculous way with the original signal.
Nothing new about that
Placing an overdrive pedal after a delay is nothing new at all.
Remembering a time, when there were no amplifiers with integrated effect loops, the guitarists used their analog delays and tape echos before the amp.
Because of the fact, that the amplifiers distorted anyway, the delays have been placed, so to say, before the “overdrive”.
The Tape Echo/ Marshall Amp sounds of Jimmy Page are a pretty famous example for this sound.
You can also emulate this combination by placing an overdrive pedal behind the delay.
Of course, not every overdrive pedal works well with every delay.
Sometimes, you will have to try out different combinations until you find the right match.
After a reverb pedal, an overdrive can also sound pretty well.
Surely, this sound is not delightful to everyone. The tone seems to be blurred but somehow also more organic.
Steve Wilson (Porcupine Tree) swears on this combination and creates unique sounds.
I recommend to try it out!