It's good that you are being specific about what you are - that's the issue I see with most online discussions and Google searches. You said you're looking for:
* multifamily/industrial
* current listings
* old listings (do you mean sold?)
* off-market
* owners' information
Based on this, I'd say you have a few good options.
First, you have to play with LoopNet - it's easily the biggest.
BUT, The CoStar Group is sneaky, and the way they work with brokers means that you will find MORE listings on CoStar.com. Also, you'll see more of the sold listings there. You only get "recently sold" on LoopNet, and the search is mediocre.
The first competitor to consider is Crexi - it's basically LoopNet but smaller. You may as well check it out and use it similarly.
So Reonomy is different. Its focus is on the data for all properties first, then on current listings. So it'll have the information you're looking for and valuable data to help you with diligence, including owner information. If you want to pay the fee, it may help you in your search. And it's more likely to help you with the off-market deal search as a result.