You can check a few things. When editing a crawled property the page will show a section called "Content using property" and will show sample document urls using the property. Do you see any urls under sample documents for these crawled properties? If no documents are using this crawled property then it is possible that documents are not being crawled. Check your crawl log to see if the documents using the multi choice column are being crawled. The "InvalidPropertyException" can occur if you add a new managed property and then do a fulltextsql query before the cache is updated or there are no documents linked to any of the mapped crawled properties. You can try doing an IIS reset to force a cache refresh and try your query again. Otherwise it is probably because no documents are using any of the crawled properties.
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