I am a beginner/novice, so take my learnings with a grain of salt. I have a similar situation. The black stuff under the linoleum is termed cutback adhesive, and may or may not have asbestos in it. Some pro-sanders will offer to sand it out. The ones I interviewed didn't love it, but didn't seem concerned about it. They couldn't gaurantee the finished results though. They usually will not gaurantee the finish, since the adhesive may be inbetween the boards and might outline the boards after sanding. I also heard that the sanding could heat up the adhesive, and melt it further into the grain or between the boards. This may or may not be apealing to you, and may look awkward if the boards transition into an area where no cutback adhesive was used.
Regarding asbestos, apparently this naturally found material has different species of it ( six or so), where some are more dangerous than others. It doesn't look like the EPA cares if it is one version versus the other. They seem to clasify situations as either having asbestos or not haveing asbestos present. EVERYWHERE you read online will say it is friable and absolutely should not be sanded. As mentioned above, the pro sanders I spoke to thought otherwise, but then again they do not have to live in the place after they are done with the job.
If you scrape it with some sort of solvent present, it should not be as airborne as when sanded. The rental companies will likely not recommend that you sand it with their machines, in case the cutback adhesive does have asbestos present. Also, their drum sanders may not be strong enough to take it off, but that you will have to check on. If you do decide on having a pro sand the adhesive out of the wood, it would make sense to vacate the premesis until a few days after they are done. I have read that some strands of asbestos can take three days to drop from the ceiling to the floor due to their extremely low density. This was a little shocking to me. Upon arriving back in the home, it would make sense to thoroughly clean the house and avoid stirring up the place until it is clean, since asbestos seems to be very light and easiest to address when not airborne. If you have kids, I would think carefully about your options. Many people end up removing the wood or covering/encapsulating it ( to seal it). If this type of situation was in a public place or a school, different rules and laws apply and costs to deal with your situation would likely escalate exponentially.
Going back to my experiences, I too tried using removers available at the local paint store, but didn't have success. An experienced poster recommended SoyGel made by Franmar, but this may be hard to come by unless you are a pro.
When I tried to remove the adhesive with consumer-type removers, the adhesive just became gooey and smeared. I tried a floor scraper and that worked very well (was easy to get to the hardwood, but would have been too tedious of a job for the situation. I eventually will be removing the mystery adhesive and the red oak it is bonded to with a power handsaw and a friend holding the shop-vac at the blade to collect the dust immediately during sawing (both of use wearing dust masks of course). My wood will be replaced with new 3/4" red oak.
You may want to read the following posts too, and talk to a more experienced professional on this topic, as again I am casually new to this forum and wet behind the ears on most if not all related topics.
Good luck.
http://www.hardwoodinstaller.com/hardwo ... ht=cutback
http://www.hardwoodinstaller.com/hardwo ... ht=cutback
http://www.hardwoodinstaller.com/hardwo ... ht=cutback
http://www.hardwoodinstaller.com/hardwo ... ht=cutback