Also, It will be a few days before I can get anywhere near a place that carries bike oil. Can I use CLP *** cleaner as a temporary substitute?

In my opinion, CLP is fine; certainly better than nothing. And I wouldn't go to any lengths to remove rust from a chain; if you work it so that it moves freely and keep it lubed, normal wear will remove the rust from wherever it needs to be removed. The alternatives, like phosphoric acid or abrasives or electrolytic conversion, all seem to me much worse for the chain's function than just letting it wear off, and more trouble than a new chain.

Any kind of oil is better than nothing. Whatever you have available.

Remove ? probably not entirely , throw the chain in a bin and try to keep the replacement oiled better next time ..

This .. at least you will coat the current layer of rust.

You may have sorted this, but if your chain is truly rusty but you still need a bit more life out of it before it goes in the bin, I'd recommend WD40. It'll uncease it and get it running again. It won't really do much to lubricate it though, and may only partially work for keeping the water out in the long run.

How about heavy oil like motor oil? Or do the detergents do more harm than good?

Motor oil won't flow in between the plates (where it's needed) and will attract dirt to the outside, creating a layer of dirty goop. A light oil applied to the outside and then the excess wiped off is better than nothing. As Fiets said, a rusty chain needs to be replaced.

Beware: questions of chain lubrication on bicycle forums are often endless debates.

Buy a small jug of Evaporust, pour it in a small plastic container, and submerge the chain in it. It will eliminate all of the rust, likely within a couple of hours. Then lubricate it with your choice of lubricant. Use what you feel works best for you, the whole point of a lubricant is to create a lubricating film between moving metal parts. It will need to be relatively thin for a bicycle chain.

In a pinch, you can use motor oil, it's clean a bit and lubricate until you find your bike lube.

CLP is great stuff. I use it on the bike, fishing reels etc....