"Soft" inquiries should not lower your score. "Hard" inquiries can, but that should only come from you actually attempting to borrow money or at least opening up a dialog with a mortgage lender, etc.
First, to stop this happening again, you should "lock" or "freeze" your credit report with all three bureaus. That prevents anyone from making a hard inquiry unless you unlock your report first. All three bureaus offer some kind of "lock" service that allows you to unlock and lock your credit report on their web site or an app. Usually as a come-on to a subscription credit monitoring service, but you can get the basic service for free. A "credit freeze" is more or less the same thing but is regulated by the Federal Government, while the lock/unlock offered by each bureau can have different terms and conditions; make sure you understand the difference and request the type of block you want. Note that if you lock your reports, you won't be able to apply for a mortgage or fill out a rental application. But you can unlock your report the day before you fill out the application, and re-lock it after the inquiry hits.
Then, you can try calling or writing the credit bureaus to complain. Get your reports and find out who made the hard inquiries. Write to the credit bureaus to explain that you never applied for credit and never authorized the hard inquiries. They might take them off your report. You may also be able to file complaints with the consumer protection agency in the state in question, about the companies that made hard inquiries without authorization.
I doubt it was the real estate agent who snitched on you but a "moving service" sounds like the place that did it. If you signed up for an online service promising to connect you with movers, who knows what else you agreed to. They get paid by running ads and selling your info. You can give them a bad review on Yelp, or if you have a lot of time on your hands, you could write (or tweet or facebook) to all the companies that bombarded you with ads and explain that you will never do business with them as a result of the situation, they should have used a less shady ad broker.
