I do know Multiple dex problems have been reported a lot of times before, but none of the solutions seems to work in my case.
Console:
Unable to
RESOLVED
bolts-android library was the real trouble here. There were two different versions of it causing a conflict. The FacebookSDK library brings bolts-android-1.1.2, and android-support-v7-appcompat brings bolts-android-1.1.4.
I unmarked Android Private Libraries container in the FacebookSDKlibrary project, which contained bolts-android-1.1.2. As a result, my project now had only one version, bolts-android-1.1.4, settling the conflict. It runs fine now.
Also, turns out, the duplicate android-support-v7-appcompat entries were not an issue.