I had to laugh because I have a somewhat similar situation.
Until a week ago, had 6 cars, 5 registered, 4 drivable:
2009 Ford Escape (66k)
2005 Volvo S40 (179k)
2002 Ford Focus ZX5 (115k)
2001 Dodge Ram Cummins (151k)
1987 Mercury Grand Marquis (83k)
1974 International pickup 4x4 (??k)
Anyway we sold the S40 because of its high cost of operation and still relatively high value (relative to the Focus), and the Ram because I was barely driving it and a trailer would serve 95% of the Ram's ability. The Grand Marquis was my grandpa's so sentimental attachment means it isn't going anywhere, and I'm on the fence on the IH. It has some sentimental value but is in little bitty pieces right now so to make it useful would require hundreds of hours and many thousands of dollars. Not really my bag right now. Kind of like your situation.
Just sharing.
In any case If you have no real connection to the C10, it needs work, I say let it go. No real use to having it. Pickups are nice but a small trailer can be towed behind a car and for bigger jobs (e.g. towing), Uhaul rents pickups that tow for $19.95/day plus mileage.
The Impala I'm on the fence about. Could last awhile yet or could need a litany of repairs. I'd probably just drive it until a major repair is needed (e.g. engine or transmission). Then sell it for cheap (even needing a major repair it's probably still worth a grand). Or scrap it for around $300.
The Intrepid depends. I'm not a huge fan of the older Chrysler stuff especially the transmissions. And as someone noted that stuff doesn't like to sit. So it sounds like you are going to have to exercise the car a bit which means more money spent than now. If you felt good about the reliability, especially for the near / medium term, maybe getting rid of the Impala and driving this one wouldn't be so bad. And if a major repair comes along, sell it cheap / scrap.
OK, so next option. You said you just bought a house that needs a bunch of work. You probably don't want to jack around with car maintenance. Maybe you can find one newer (2000's) vehicle that is reliable, efficient, and useful. I think a cheap hatchback that can still tow might be a good option. Honda Fit, Ford Focus, etc. Even an Accord wagon or a Honda / Toyota / whatever minivan might work well. I don't yet have a trailer hitch for my Focus but I fold down the rear seat and can easily fit 10 bags of mulch below window level (it's about a 3.5 x 5 foot load area). Obviously hauling 2x4's and plywood / drywall sheets inside is an issue, but a roof rack or small trailer would be ideal. A FWD crossover might also work. Saturn VUE's are cheap, I also see Equinox's cheap as well. We have an Escape which fits even more than the Focus, is FWD, manual transmission, and gets just 1 MPG less than the Focus at around 27 MPG average (I'm not saying that 27 / 28 MPG holds a candle next to new cars or older hybrids but they also don't have the new car price). Just a thought.