Best season to move to Ireland

Because it rains all year round, any season is best (!)

unlike India and other SE Asian countries rents do not fluctuate and are government regulated for the period of the tenancy (6 months or one year.
You cannot barter/negotiate rents.  They are as advertised for the fixed period of the
tenancy.

not really - jobs are available not on a seasonal basis but based on economic and industrial factors relating to the Irish economy.
In the countryside there is seasonal work for picking strawberries, apples, but because the wine and export markets are dairy and processed food-based, work is fairly regular.


Apart from St. Patrick's Day, these days, not really.

There is a thriving cultural and artistic community near the city centre.
Plays and artistic meeting events are advertised in cafes and on community websites.

I am slightly out of touch but so much of these events are commercialised these days
you are better finding a good Cafe where artists ''hang out''.
I don't know one by name but i can give you a recent example.
I was in the Dominican Republic over Easter.
I stayed in the Old Colonial Zone - a very beautiful part of Santo Domingo.
(Sadly the crime rate is far too high in SD.)
I found the artists quarter during the day and immediately ''networked'' with two artists (a guitarist and a poet) over several beers who invited me to their ''hangout'' restaurant
in the evening.  This was one of the  best places for poets, painters and musicians.
If I had stayed longer I would have thoroughly enjoyed the ambience - but I was on a short stopover, sadly.
So just going into a cafe (with noticebaords - if it doesn't have a noticeboard it is just another trendy over-priced restaurant)  in a popular artistic zone (such as ''Temple Bar'') will set you in the right direction.

There are no times to avoid moving to Ireland.

there is no ''cattle stampede'' to get in or out of the country
(sorry!; there are a few times to miss: if you want a quieter life - avoid St Patrick's Day and the Football Match final fixtures (Irish nationals fly into the country just for these events) together with Phil Collins or the Kardashians or Oprah coming to Dublin - hotels will be packed to capacity near the 02 or wherever else they are appearing.)
These are very popular times so everything tends to be booked out - hotels etc - for the festive occasion.   

I am currently in London but was born in Ireland and go there regularly.