[TitaniumTT]

If you call just about anyone that builds harness's, they should all tell you the same thing - CRIMP>SOLDER. In ANY circumstance. I questioned this even when dealing with the heavier gauge battery type cable... bigger than 8ga, and they say the same holds true. So I went out and dropped $80 on a lug crimper. MOST of the crimpers that you'll need are going to be around the $50 range if you hunt around. Most of the crimps I bought were from either Terminal Supply Co, Waytek. There was one co that had a REALLY nice buttsplice connector, I can't remember the name of it, I'll have to look at it when I'm in the garage next. The only time crimps are going to run you more than that are going to be in the mil-spec variety and I've been told that there are other/cheaper alternative than the Davis Manufacturing crimps.

So, you had mentioned the engine bay sensor. If at all possible I would cut the wire to length, and use the proper connector pins. You can usually crimp them with a Metri-pack style crimper. I use the metri-pak connector for metri and weather pack terminals. It can be found here
http://order.waytekwire.com/productd...%20PACK%20150/
but I know I searched around and found it for $80

If that doesn't work becuase the wire can't be extended, or its a mazda terminal, then you need to butt-splice them in. I personally, when wiring a car, use the un-insulated butt-splice stuff and just heat shrink it. I buy poly-olefin non insulated by the 100' spool and use that everywhere but the engine bay. Unless it's going to be loomed over with something. In the engine bay in an unprotected situation, I buy the adhesive lined stuff. If I'm wiring a boat, I use the retardedly expensive heat-shrink terminals. The only reason I do this is becuase most of the boats I wire are commercial and need to be coast-guard inspected. The CG generally doesn't approve anything that isn't individually heatshrunk unless it's an approved OE harness.

Connectors can be found here -
http://order.waytekwire.com/products...%20Connectors/
Crimps, these are the ones I'm not sure about, I paid $60 for them, will have to ge the name. It's a local co up in North Haven CT too. But, they're along these lines.
http://order.waytekwire.com/productd...IMPING%20TOOL/
except I paid $50. They do non-insulated butt-splice connectors. I also have a set of insulated butt-splice connectors for the marine stuff.

In your second situation, two wires on one side, one wire on the other. There is a special connector for that. Terminal supply co sells them as well and I believe a little cheaper. Either way, here is what they look like.
http://order.waytekwire.com/products...%20Connectors/
Basically, you would use one that has an 18-22ga (red) on one side, and a 14-16ga (blue) on the other. The factory wire would be cut and stripped. The additional wire would be spliced with the factory and then inserted into the blue cavity and crimped. Don't forget to put your heat-shrink on. Then the other side of the factory wire inserted into the red cavity and then crimped as well. Heat the shirnk and you're done.

I've had the solder vs crimp debate with alot of people. I've never had a crimp fail. I've had solder joints fail. I've also over crimped a wire and cut the strand, but that was only once.