Each WiFi "channel" spans a certain range of frequencies around 2.4 GHz, and it's possible that both networks are configured to use the same channel. There are utilities you can use to determine what network is on what channel, and you can change your own network to a channel that is not being used (or with lower interference) for the best performance.
You can use a tool like inSSIDer (as you listed above), or in some cases, the WiFi card manufacturer may provide a similar utility. There are also a wide variety of alternatives to the tool I listed above.
As for why the low signal network affects your high strength one, the key fact is that "noise is noise". From your perspective, any transmission not from your network is considered random noise, and will corrupt packets. If a network on the same channel has a 30% signal strength (assuming both networks are transmitting packets at the maximum rates), this introduces 30% error into your signal (assuming the 0's and 1's being transmitted are truly random).
Thus, 70% of your packets still arrive fine, but the remaining 30% need to be re-transmitted, affecting the total available bandwidth for your network.