For the variables in exp() in the model block, are the simulated moments for those variable in exp() measured for their log values or their log-deviation ??
All moments in Dynare are always for the actual values of the variables. If the variable is a log-level (due to the exp-transformation) the mean will be the mean of the log-level. For second moments: they are centered moments. The centering takes the mean/steady state out. At first order, the second moments from log-levels and log-deviations from steady state are thus identical. Only at higher order, there would be a difference due to the mean not being identical to the steady state.
so, if the order is 2.
then say the model block declares variable u as exp(u).
Then its empirical standard deviation is underroot(1/n(summation(ui - ubar)^2))
where ui are the logs of simulated ui, and ubar is the empirical mean of log u.
So we can say that the standard deviation of log u is a deviation from its mean in the simulated data ? Am i right ?
Yes, and as everything is in logs, it has the interpretation as the standard deviation of the percentage deviation from the sample mean.