No, he can not. He didn't break Jiraya's Genjutsu.
So he mos def can'tstop Itachi's Tsuk.
That's different. Jiraiya's genjutsu was
AUDIO, while Tsukuyomi is
VISUAL. I DO believe Nagato can counter VISUAL genjutsu because the Rinnegan IS the ultimate dojutsu and tecnically the true final stage of the sharingan, although not directly related. Being an advanced sharingan, it should in theory be able to counter sharingan genjutsu along with other visual genjutsu.
As for Mr. Oblivion, Jiraiya's genjutsu was different. Until the Rinnegan becomes the ultimate EAR, it OBVIOUSL
Y isn't blocking Ma & Pa's Frog Song Genjutsu.