OK, I've been asked to make my comment an answer, and I can write something that may or may not be helpful to you, but it won't speak specifically to the goal of motivating your team, so I expect to get a lot of down votes on this.
There are several possible scenarios, and probably most of them have more negatives than positives for your team.
1) The company is being acquired
This is the scenario I alluded to in my comment. If you're in a startup, these shares are probably kind of "vapor." Your vesting scheme means that it will be a long time before you get any of them, but they don't actually exist until there's an IPO or acquisition. What I saw at the startup where I previously worked is that there was a mass layoff before the acquisition. My suspicion is that shares that didn't exist at the time of termination were not credited to the employees that were terminated, regardless of vesting status. I had left previously, so that is only suspicion. However, in this age of acqui-hires, why else dispose of a large part of your assets?
If your company has a "no vacation policy," keep in mind this means they don't owe you anything for the vacation you didn't take even if you have never had a vacation in 4 years.
The positive of this situation is that after a visible IPO or acquisition, recruiters will be all over ex-employees. So as long as you have savings to last you a couple of months, you should be fine.
If you survive the acquisition, you will also be sitting pretty as your equity also suddenly materializes and you'll probably be asked to sign a contract to stay at least some number of months or years.
2) The company is tanking
In this case, management is trying desperately to do whatever they can think of to stay afloat. The odds that they will succeed depend on how in touch they are with what is really going on in the business.
In this case, if the business sinks, you'll have no equity, no job, and no recruiter beating down your door. If it swims, there's a slight chance you'll earn someone's unending gratitude and be the golden boy for a long time.
3) The upper execs are padding their own salaries by forcing everyone to do more with fewer resources
Not much to say here. Possibly longer term they'll realize they're shooting themselves in the foot and back off. By that time you and your team will likely be burned out.
What to do
It's hard to really know what is going on behind the boardroom doors, so you need to look at solutions that cover every eventuality.
You should emotionally disengage from your job. Part of the reason this is bothering you so much is because you're too into it. I was laid off from the startup I mentioned after the software was feature-complete, but about 5 working days shy of having a releasable product. The lack of closure had me dreaming of this job for months, trying to go back and finish the project.
Also, you'll be able to do a better job for your team if you have some emotional distance and you're not so miserable. If you've ever worked out your 2 weeks' notice, remember that feeling and apply it.
Save every penny you can get your hands on. Best case if you lose your job is an interview within a month and walking through the door within 2. Make sure you can pay your bills for at least 2 months without income, preferably more. Seriously, cut coupons, don't flush just for pee, quit going out to eat, limit trips in the car to save gas--anything you can do.
If your situation is such that it seems worthwhile to stay, then polish your resume and update your LinkedIn profile rather than moving immediately to apply for new jobs. If you have decent savings, this might be a good way to go anyway, as you're always in a more powerful position when the company is contacting you.
Connect with everyone you can in the company through LinkedIn. This may come in handy if you get laid off. For instance, once I got laid off and it turned out something like 80% of the people laid off were women or people of color, even though we were a far smaller fraction of the workforce. I didn't care because I had a job before my severance ran out, but this kind of information can be useful if you need it.
If there's an equity situation, talk to a lawyer ASAP. Even if not, you may want to speak to a lawyer or career coach about negotiating the best exit deal possible. Yes, you can negotiate this. This is especially true if you are older, a minority, a woman, or have some "special status" where the employer is worried that you might have grounds to sue.
If your company has a "no vacation" policy, balance your desire to keep that job with what you need to do to stay covered in the event that you lose your job. Rest assured the company has no intention of paying you for vacation you were nice enough not to take.
To the original question
You may find that simply talking to your employees and allowing them to express their fears helps, especially if you can help them work toward solutions. You probably shouldn't share anything I've said above except "save your money." :-)