Can the internal energy - work exchange take place in an isolated system Isolated System is a system through which neither mass nor energy can pass. According to this definition, could it be implied that although we could have no energy exchange, we can exchange Internal Energy for work, as in a adiabatic process.
Alternatively, can a closed system undergoing adiabatic process, be considered as an isolated system?
If not, kindly provide a universally accepted definition of isolated system.
P.S:- Wikipedia states contrasting definitions for isolated system and thermally isolated system
 A: Strictly  speaking, in physics an isolated system is a system which has no contact with the external world, including the possibility of exchanging work.
However, as in many other examples, sometimes the technical meaning in physics is not the same as in everyday language and the two semantic basins may cause some ambiguity. In some cases, we use the term isolated as synonym of a system which cannot exchange heat and particles while its walls can move. Moreover, is some contexts, isolated may be a shortening for thermally isolated.  Therefore, it is always a good idea in physics to  state explicitly the precise meaning of the term.
A: 
Isolated System is a system through which neither mass nor energy can
  pass. According to this definition, could it be implied that although
  we could have no energy exchange, we can exchange Internal Energy for
  work, as in a adiabatic process.

An adiabatic process is one in which a system does not exchange heat with its surroundings, but in which there is work transfer between the system and its surroundings resulting in either an increase or decrease in the internal energy of the system. Consequently, an adiabatic process, as it is generally understood in physics and engineering, does not involve an isolated system, as is generally understood in physics and engineering.

Alternatively, can a closed system undergoing adiabatic process, be
  considered as an isolated system? If not, kindly provide a universally
  accepted definition of isolated system.

A "closed system" as is generally understood, is one that does not exchange mass with the surroundings. But a closed system can exchange heat and/or work with the surroundings depending on the nature of the system boundary and how the process is carried out. 
In the case of an adiabatic process, either the boundary between the system and surroundings does not permit heat transfer (e.g., a perfectly thermally insulated boundary), or the process is carried out so quickly that there is insufficient time for heat to transfer. In either case, there is work transfer between the system and surroundings. For a system to be "closed" is a necessary, but not sufficient, condition for a system to be isolated. To be isolated the boundary must, in addition to being closed, not allow any form of energy transfer (heat or work).
I can't say whether or not there is a "universally accepted" definition of an isolated system. But for mainstream thermodynamics, it is a system in which there is no exchange of mass nor any form of energy between the system and surroundings. 

P.S:- Wikipedia states contrasting definitions for isolated system and
  thermally isolated system

Contributions to Wikipedia come from many different sources, not all of which are necessarily the most reliable with respect to a particular area of physics and engineering. But the adjective "thermally" in connection with "isolated system" only infers, at least to me, a system that is adiabatic (no heat transfer). It does not address the need for no work or mass transfer to be  qualified as "isolated".
Hope this helps.
