Have some problem to understand difference between subject. It all means scream, but I suppose with some difference. I'll write what I think, correct me, if I'm wrong.
Strillare - scream, but very high voice, like ultrasound )
Urlare - see no difference with strillare, but more like "howl"?
Gridare - i see in dictionaries mean "scream", but I think main meaning is(
well I don't know english word either, but can assume) "berating someone".
Sgridare - gridare with higher voice?
Rampognare - have no idea what difference with "gridare"
P.S. I can't use monolingual dictionaries. Not enough knowledge.