In some respects the two styles of music are not so different (depending, of course) on what you consider 'pop' and what you consider classical. But, there are elements of each that can be found in the other.
One of the reasons so many classical vocalists stray into singing pop songs (I'll include Broadway tunes in with that category as most don't consider the songs from Broadway in the Classical Genre) is because their well trained voices can add power and emotion to the music and yet, singing these pieces isn't unfamiliar from what they sing normally. It can also be a lot of fun, letting your hair down sort of thing.
Numerous orchestras perform 'pop' concerts, and there are even famous 'pop' orchestras. Jeff Tyzik of the Rochester Philharmonic Orchestra understands that "One loud snare-drum hit is louder than an entire string section. So it's technically impossible to balance an orchestra and a heavy-metal band." However, there are ways to blend the styles and that's where orchestration and technology play a role.
Heavy-metal, as an example of pop, stems from a fusion of blues and rock, both have their roots in classical music. The rhythms used in heavy-metal are nothing different that classical musicians have been playing for years. The driving beats we might associate with a Black Sabbath isn't all that different than the driving force behind Beethoven's 5th Symphony. Led Zeppelin occasionally used irregular rhythms, but in a repetitive manner, not unlike what Holst does with Mars. So, if you're trying to orchestra a heavy-metal piece for orchestra, the rhythms are pretty straight forward, just be aware of where the accents are in the music.
Distortion can be somewhat problematic, as heavy-metal uses a lot of electronics, and the nature of amplified sound, to create the music. However, numerous classical composers have used techniques like sul ponticello to get a different sound from the strings. Putting the low strings on a root note and the low brass a semitone up creates a nice warring sound between the sections, while maintaining a sense of the root. Add the same sort of effect using high winds split between two very high notes a semitone apart and then tremolo the high strings across the same two notes and you'll get a shimmering shrill. There are lots of other ways to play with sound to get a unique tonal color that emulates the biting sound of heavy-metal without using amplification.
Of course, you can use amplification and electronics too. Numerous composers since the 60's have been incorporating electronics into their compositions. So, if what you're trying to do is re-create an electronic sound, sometimes using the same electronics as in the original sound overtop an organic sound of the orchestra can be very new and yet, indicative of the original. Amplifying some of the instruments can also drastically alter the sound, as there are a number of effects that can be applied to the amplified sound making it unrecognisable to the original. However, the full force of an orchestra can produce a great deal of sound and amplifying the entire ensemble would not necessarily be effective (and would be very expensive). So, perhaps in all things, think moderation.
In the end, have fun, fun with the music, orchestrating music you enjoy, creating a "cover" for your favorite piece but for an orchestra. Be inventive, don't just stick with putting the loud bits in the brass, and the soft bits in the strings or woodwinds. Use percussions, use it lots and often. But most of all explore not just classical music, but classical instruments with all kinds of different forms of music. You'll be amazed at what you might find.
There is a group called Trans-Siberian Orchestra which plays symphonic rock, which is rather like 'Phantom of the Opera’ meets 'The Who'. They've sold millions of records, so not is this sort of thing fun, it can be profitable too.