Real Exchange Rates calculation
you cannot compute real exchange rates based on the data you have. What you can do, and what is often done (not sure what it is good for though) is to use relative PPP to calculate changes in RER using some base year. 
The OECD publishes some statistics on P*/P, you could also use that, although I am not sure what methodology they use. 
In practice, you would need the actual prices of a basket of goods to calculate the RER, once you somehow normalize prices within a country you can no longer calculate the RER.
hence the appeal of stuff like the Big Mac Index.