Toumpas played 10 games for the Power after joining the club in 2015, following three seasons and 27 games at Melbourne.
The 24-year-old was selected with the fourth pick in the 2012 AFL Draft.
Irra failed to play an AFL game during his two seasons at the club.
Port Adelaide’s General Manager of Football, Chris Davies, thanked the pair for their contributions to the Power.
“Jimmy and Emmanuel have given great service to our club both on the field and within our community programs as leaders in the multicultural space,” Davies told portadelaidefc.com.au.
“But, we have reached a difficult time of the year when the club needs to make decisions for its future regarding our playing list.
“We thank both players for their professionalism and we wish them well for their futures.
“Both Jimmy and Emmanuel are always welcome at the Port Adelaide Football Club.”