I just bought a new Sony Xplod stereo for my 2006 Mitsubishi Lancer. My old system was an Infinity, which from my understanding uses it's own amp (under the driver seat) and would not work with the Sony. So the techs had to run new wiring to each speaker (the speakers and sub woofers are also Infinity). I'm assuming they disconnected the infinity amp...The sound quality was greatly diminished because the speakers are only running off the built-in amp on the Sony head unit. I can barely get the volume past 15 without the back speakers crackling and sounding distorted. The bass from the back speakers and sub woofer was definitely better on the factory system. I was wondering if it's possible to install an aftermarket amp to get the quality back. I have 4 speakers in the front, 2 in the back, and 1 sub woofer in the trunk. What would be my best option? I really know nothing about car audio but my new Sony Head unit info is:

Power Output: 17 Watts RMS X 4 at 4 Ohms <1% THD+N
SN Ratio: 82 dBA (reference 1 Watt into 4 Ohms)

I would really appreciate any help you can give me. Thanks in advance.

Sony... thats your first problem.

I will answer your questions in the order they are in your post.

A. Yes, your infinity system uses its own amp. It powers about 25rms to each speaker
B. You can integrate the amp into your new speakers, the techs you went to screwed you over. They just wanted to make more money by running all new wire.
C. The system power has been greatly diminished, as has the quality. This is because you are running 6 speakers on a cd player meant to power 4 speakers.
D. The bass and quality in the back speakers and sub is better stock because of the same reason posted above, and because you cannot hook a new head unit up to stock stuff. It just sounds terrible. Much like putting in new speakers with the stock head unit.
E. Best option is to get a 5 or 6 channel amp, many companies carry them. Go to www.sonicelectronix.com to find one that you want.
F. To get the sound for your sub back you will need to get a decent mono amp. Goto the same sight listed above.

Well, the speakers weren't new. Everything in the car was infinity factory. All that was changed was the head unit. They said they had to bypass all of the factory amplifier.

Look at letter B.

You do NOT have to bypass the amp. You integrate it with an integration harness. The shop you went to sucks. Never go there again.