I am looking to buy a new receiver which is HDMI compatible. I have a Sony DAV-DX375 Home Theater System. I'm curious if I can use these speakers and subwoofer with a new receiver. If so, what specs do I need to look at to make sure it will work optimally. The receiver I'm looking at says it has 7.1 Channel Power Rating: 105W x 7 Amp Power (8 ohms, THD 1.0%) but the specs on these existing speakers are 3 ohms and the subwoofer being 1.5 ohms. Will this work and if not what impedence of speakers and sub do I need? Thanks in advance for any advice.
Receivers get rated at a specific impedance load because they're required to by law. That doesn't mean they won't drive speakers of differing ohm ratings. Very low ohm speakers can cause an amp to over-heat, shut down, or fry at very high volume levels. As long as the receiver is well ventilated and is used at reasonable volume levels, you will be OK. Look at it this way -- the amp in the old Sony receiver that came with this system is certainly no better than the amps in most entry level receivers, and the Sony drove those speakers OK, didn't it? If you do make this switch, don't use the speaker wire that came with this system. Use the thickest wire that will fit the clips on the speakers (no smaller than 16 gauge).
There is a problem with your plan, however. The subwoofer in this system is passive, meaning that it needs an external amplifier. Most, if not all, surround receivers do not provide an amp for the subwoofer because most subs have their own built-in amp these days. So you'll have to upgrade the sub to a powered one. And while you're at it, you should upgrade the rest of the speakers as well.