Is there any easy and systematic way to analyse circuits containing opamp and multiple diodes?
Yes, all the standard rules for Opamps still apply, so, 


no current flows into inputs
differential amplification is very high


And other than that, a simple "diode current is an exponential function of voltage" does the job pretty well. 


  systematic procedure then hit and trial.


Then simply make a graph for your input voltage(s) and try to figure out in what operational state the diodes are (blocking, reverse breakthrough, linear forward bias, saturation).

You can basically make a table with all possible state combinations for all your diodes. Depending on how you model your diodes, that might be quite a few! Then, check by which input voltages these states can be achieved (or whether they are possible at all).

That's the most systematic you can do without doing a full parameterized simulation: 

The "really" systematic procedure is writing a SPICE simulator or something similar.

Since you're clearly a student of electronics, the reason why you're looking at these circuits is to learn the tricks and higher-level patterns from which such nonlinear circuits can be built. The whole point of this exercise is that you don't need to do a systematic analysis – which would be so computationally intense that humans use computers to do them.