For a bike from the 70s and 80s, the mantra was that you could usually replace the freewheel without replacing the chain. But if you replaced the chain you should replace the freewheel also. Freewheels wore faster than 5- and 6-speed chains, and an old freewheel wouldn't mesh properly with a new chain. Now the situation is reversed, and cassettes last much longer than chains if you replace the chain regularly before it's too worn. 9- and 10-speed chains are much narrower than the old chains and don't last more than ~1500 miles. Chainrings should last much much longer than chains or freewheels/cassettes.
My advise is to not replace your chain or freewheel until you have problems. When the chain starts skipping across teeth on your freewheel, replace them both. What replacement parts do you have? If they were bought in the last few years, you may have an 8-speed chain to replace a 6-speed chain, and those 8-speed chains have a pretty short life, in my experience. Once you go that way, you'll be replacing both chain and freewheel every couple years, and given the availability of freewheels these days, I'd hold off as long as possible.
Regarding chainrings, you have to look at them separately. If they've worn to where the teeth are needle-sharp or the chain doesn't sit firmly in the bottom of the space between teeth, then replace them. When you put on a new chain, check that it seats well in the chainrings because the old chain was stretched with more spacing between links.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72