Introducing novel genes to an adult multicellular organism?
Short answer, in theory yes, in reality, at the current state of the art, no.

I guess you are speaking about higher organisms (such as mice or humans), if you are referring to small non-complex multicellular organisms then the answer is yes as far as you can transfect every cells with the system described hereafter.

The most promising technique is using the CRISPR/Cas9 system which has already been used to create all types of modified organisms but starting from the embryo. Here a good Nature reference http://www.nature.com/nbt/journal/v32/n4/full/nbt.2842.html.

There are no ways, at the moment, to transfect an entire organism with the full system. The most recent attempts I heard off is to target specific cells using an encapsulation techniques that only merges with the membrane of specific cells therefore delivering the CRISPR/Cas9 system in a targeted manner. This was in an attempt to knock-out a defined genomic regions in those specific cells, not to introduce a new gene.

I believe in the near future that this will be possible. Not necessarily every cells of an organism but at least some specific cell types.