Is there a HCPCS code (P code) to charge for platelets that are leuko-reduced, irradiated, and washed?  

I do not see one on the 2016 list.

Is it possible to charge using 3 separate P codes, one for the platelet, one for irradiation and 1 for wash? All linked to the unique product code for that product. 

No you charge for the product, then each process.  So the HCPCS for leukoreduced platelets, washed is P9035 just like non-washed but you have 2 procedures codes in your CDM to include a larger charge for the washing then you add the irradiation using CPT 86945.  For example a regular platelet unit is procedure code 63877 and is priced at $450 but when it's washed the procedure code is 68309 and you charge $611.  We have our computer system built so that if the product code is washed then it charges the procedure code for the $611 but if it's not washed it charges $450.  Unfortunately there's only a P code for washed RBCs.