Phrase.

[OmnificienT]

qalegh,

toQDuj chaghmoHpu' SuSjev chalDaq

Is this correct Klingon? It should mean something like: The wind dropped a Bird of Prey from the sky.

yitaH 'ej yiQap!

[Qunchuy]

The SuSjev's sky-place has caused a Bird of Prey to drop [something]. Not quite what you were going for, but close.

I believe chagh drop means to cause something to fall, so the suffix -moH cause is superfluous. Alternatively, you could substitute the verb pum fall and get the meaning you intend.
The suffix -pu' indicates perfective aspect, not past tense. It's a difficult concept for some people to get at first. Past tense is often used to translate it, but unless you really want to express the "completed" idea, it doesn't really belong in the Klingon.
SuS is wind. I don't know why you tried to attach the verb jev storm to it.
The noun chal sky is neither the subject nor the object of the sentence, so it needs to come at the beginning of the sentence, before the object.
The locative suffix -Daq indicates where an action takes place or is directed towards. To talk about where something is coming from one uses the suffix -vo'.

chalvo' toQDuj chagh SuS The wind dropped a Bird of Prey from the sky.