I think Russia needs to put some thought into their response and be clever about it. The IOC's decision was made to set up Russia in such a way that they have a lose-lose scenario and terrible optics: a) admit their athletes into the games, look weak and defeated, and worst of all guilty, and expose them to all kinds of harassment, b) pull out of the games and look like they are punishing their own athletes.
I believe that Russia can respond appropriately to IOC's decision and still allow their athletes to compete. But the severity of their response has to address their own role as participant and partner in the Olympic process. I'm biased about this because I have never really cared about the Olympics and I know that Russians do. But I think it would be best for them to consider cutting off the Olympics in the long run, phase them out maybe even completely. Because as things stand the Olympics are controlled by organizations that do not have their interests in mind and unless Russia can impose its influence in any way, this will be a losing game.
So I propose playing real hard ball and threatening to pull out of the process entirely. Draw up a list of demands, among which should be that the IOC reinstate the banned athletes from Sochi unless they can prove - convincingly - that those athletes doped. This means, yes, obtaining actual positive samples. Letting this kind of stuff go creates an awful precedent for Russia, and allows these Western-controlled governing bodies to do whatever they want. If they can ban Russian athletes without concrete proof of guilt, what could possibly stop them in the future? The abuse will only continue if Russia remains subservient to this system.
By making a concrete list of demands Russia will also shift the onus from themselves onto the IOC, which I think will play well with its public. At present time Russia is running around and doing its best to adhere to arbitrary, Western-imposed standards, spending tons of money revamping its doping program. It should stop doing this and turn the tables completely. This is costing them too much money and labor and just isn't worth it.
Draw up demands, get out of the Olympics, send any local IOC bureaucrats packing and make it clear that you will not participate until those demands are met. In the meantime allow the Korea-eligible athletes to participate neutrally in this particular instance only (give the IOC a taste of what they'll be missing), but without any state funding or assistance of any kind. Give your athletes the choice to make up their own minds, but before they get there make your announcement. Announce your tit-for-tat in advance. In the meantime you will prepare your athletes (including the potential summer Olympians) about their likely non-participation in future games, but also have enough time to figure how to redirect their competitive aspirations.
Look at this as another round of sanctions. You will lose monetarily in the short run. But in the long run you will only lose to a greater extent and continue losing if you accept the existing status quo. The Russia ban only happened because the West is calling Russia's bluff, believing that Putin won't have the guts to respond. They believe he is too addicted to Western capital (I hope not).
But without Russia the Olympics will never be a complete event, and will always deal with questions of "what if." Make them feel the brunt of their decision. This is Russia's only true option.
The decision to ban Russia is an extension of a pattern of Western aggression against Russia. It is also so incredibly transparent. Even the fact that Rodchenkov is hiding in the US and working with the secret service is absurdly on-the-nose. Respond with strength or die.