Visnovsky, acquired in an offseason trade from the Anaheim Ducks, has been playing in the Kontinental Hockey League in his native Slovakia during the lockout. He expressed the desire to continue playing there even with the 2012-13 NHL season set to get under way on Saturday, but the KHL has reportedly denied his request to extend his contract through the rest of this season.
Neil Sheehy, Visnovsky's agent, tweeted earlier in the week that his client intended to report to the Islanders after dealing with some personal issues.
Visnovsky, 36, is a veteran of 11 NHL seasons with the Kings, Oilers and Ducks. He has career totals of 117 goals and 450 points in 771 games.
Strait, 25, has played in 12 NHL games with the Penguins over the past two seasons, recording one assist.