What is this fleshy-stemmed plant?
Reminds me of Senecio articulatus (Candle Plant; hot dog cactus), a succulent plant in the broad (aka polyphyletic) Senecio genus (Asteraceae). 



 Source: U. Wisconsin-Eau Calire    

Based on my limited knowledge of the plant and the variable leaf shape, I am not sure if this is your species or not. However, I'm sure some additional searching using this species as a guide will get you to the correct species/cultivar. 

World of Succulents provides some additional information on Senecio articulatus. 

You can see a video of a Senecio succulent identified as S. articulatus for better comparison to your plant: