Blender makes burning smell after liquid spilled on (maybe into) it
See if you can locate the source of the smell.  Blenders are generally designed so that a simple spill doesn't cause permanent damage, but if the connection between the cannister and the motor came partially apart when the seal broke, it is possible that the little doodad they use to interface was damaged.

I've had a burning smell before when using a cheap blender with a high-wattage motor; where the drive shaft connected to the canister was rubber or plastic and stripped, producing a burning smell and lots of little black pieces. 

Edit: Burning smell common to Oster blenders

A casual Google search shows that a lot of the Oster blenders and immersion blenders will produce burnt-insulation smells in use, some from the first day.  In your case, it may be coincidence that it started when it did, or if there was ice in your smoothie that could have been enough strain to jiggle something out of alignment and start problems. 

I'd start shopping for a new blender.  The burning smell generally means your blender's days are numbered; that smell is the motor or its insulation overheating, and death is soon to follow.  Repairing a burned-out motor will cost around the same amount as a new blender.