What is the best unobtrusive and objective method to measure mental workload? What is the current research/industry standard on measuring mental workload using objective measurements (e.g. EEG, eye-tracking)? 

Do you have any suggestions for specific tools and techniques? 
Are there combinations of physiological measurements one should consider?
There are different parameters you can use, but as the question is not clear what exactly you want to do , I think with EEG and Task Load Index (TLI) you are good to go.


  The Task load index (TLI) is the so called engagement-index  and  is 
  defined  by  two  formulas,  TLI1  and  TLI2. However, these indices
  were calculated as follows:
  
  
  where Pθ and Pα denote the theta- and alpha-band power, respectively.
  Pθ,Fz and Pθ,AFz are the theta activities of Fz and AFz electrodes
  respectively. The θ (theta) activity was calculated by averaging the
  power spectrum of the θ frequency range (4-7.5 Hz). Similarly, Pα,Pz
  and Pα,CPzPOz are the α (alpha) activities of Pz and the pool of CPz
  and POz electrodes, respectively. The α activity was calculated by
  averaging the power spectrum of the α frequency range (8- 12.5)


This section is exactly quoted from this paper.