Heh, I'm a bit late to the party on this one.
1. Squeaks on neglected bikes come from the chain 90% of the time, in my experience. Use a nylon brush and wd-40 to remove most of the crud, rinse it down, let it dry thoroughly, then apply oil on each roller. I like tri-flow, 3-in-1 will also work, whatever light oil you already have. I've even heard of people thinning 5W30 with paint thinner. For a cheap bike I'm sure it's fine. After applying, spin the pedals a bit then wipe off the excess oil.
2. Since you said it seems to come from the front, headset is a possible culprit, as is the wheel hub. Honestly though, I've never had either of those squeaking. You could open them up, clean then grease. Again, for grease, whatever you have on hand is fine. I use a tub of auto-parts shop bearing grease. White lithium from the hardware store is fine too. You could even change the ball bearings while you're at it, loose balls shouldn't be terribly expensive from an industrial supply place or your LBS (or VXB), maybe 5$ for a headset rebuild. If the races are shot though, and it's a wal-mart type bike, you're likely out of luck for a replacement. These bikes often used non-standard parts. Still, cleaning+grease will get rid of the squeak, and no kid cares about incredibly smooth steering.