I will likely be taking a work assignment that will involve relocating to Southern CA (Carson CA area) for six to nine months. I am thinking about using a bicycle to commute to work.

I currently have an old Ross steel-frame 10-speed bike (friction stem-mounted shifters, suicide brakes) that I bought new back in the 70's. Although I no longer ride it any longer - old legs need more gears on the hills where I live - I'm thinking about hauling it out there and putting it to work. The bike needs a really good lube and tune-up though. What sort of tools would be needed to disassemble the bottom bracket, wheel bearings, etc?

Park used to have a better list of tools, less so now, but still some decent repair help. There's plenty of internet info (Sheldon Brown, etc.) and lots of simple how to books (Bicycling Mag, Lennard Zinn, etc.) that all have tiers of tools. Also maybe some coop places where you can share tools, or a bike maintenance class at an REI, etc.

You're probably going to need <$50 of bike specific tools -- some a good general investment (cone wrenches, chain whip) others possible specific to your older bike (BB and cassette tools). You'll need to buy cables, tires, tubes, maybe tape, grease, ball bearings, perhaps some races, etc. depending on how rotten all is, probably in the $50-100 range. At the end of the day, this is eminently do-able but also likely in the same ball park where you might find a more modern, capable, and perfectly functional used bike. Reach your decision point on that before you go hunting for some archaic tool that a newer bike wouldn't need, although many of the simple cheapie all-in-one bike tool sets will come with much of what you need.

PS https://sheldonbrown.com/tooltips/index.html

Closer to the era of your venerable steed

I'm going to recommend some reading rather than specific tools. If your bike has cottered cranks for example, you're going to need a different set of tools than if your bike has more modern 3 piece cranks.

I would take a look at Sheldon Brown's website. A book called "Zinn and the Art of Bicycle" maintenance might be very helpful too. It would be great if it could be found at your local library.

Cone wrenches for wheel bearings are pretty generic but removing freewheels takes a tool specific for the type of freewheel you have. Some bike shops will take the freewheel off for next to nothing. You might want to see if you can find a Bike Co-Op near by. One near me has work space available for rent and is stocked with commonly used tools.

Yeah, go to the Sheldon Brown link posted above. Also, the Classic and Vintage, Mechanics sub-forums should be helpful as well.