>>Add a new step 1. Remove the quarter round and baseboards
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>Neither of those to worry about.
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>>and cut the bottoms off the door and closet molding (assuming you've already pulled the carpet) to the height of the new flooring.
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>Is there any power tool that can do this? Or do you have to get handy with a hand saw or even a hack saw? It seems like the cuts will be too low for a power jigsaw or circular saw.

I use a Mitre hand saw. It's really not that bad, but you pretty much have to lay down on the floor (using a small piece of the flooring, as Jay suggested) in order to make sure you're getting a good straight cut.

I would not use a hack saw. It's teeth are real fine, for cutting metal. You can get a fairly good Mitre saw for $10.00 (U.S.) or less that will make quick work of the job.