Ydinvoiman vastainen mielenosoitus keräsi satoja Helsingissä
Useita satoja ihmisiä kokoontui ydinvoiman vastaiseen kynttilämielenosoitukseen Helsingin keskustassa tiistai-iltana. Ympäristöjärjestöjen tapahtumassa muistettiin Japanin luonnonkatastrofin uhreja.
So far I can't seem to quite understand the word, vastainen
I think this simply means:
Ydinvoiman vastainen..."Anti-nuclear"...
So the headline is:
"Anti-Nuclear Demonstration Gathers Hundreds in Helsinki"
The first paragraph is interesting grammatically, and I assume is very typical of well written Finnish....???...plenty of use of plural partitives and genitives....

Useita satoja imhisiä kokoontui ydinvoiman vastaiseen kynttilämielenosoitukseen Helsingin keskustassa tiistaiiltana.
I think this is an existential sentence...I say cautiously...

"There were gathered Tuesday evening in Helsinki's centre many hundreds of people to an anti-nuclear candle demonstration."
...and in more typical English:
"Many hundreds of people gathered Tuesday evening for a candle-light demonstration in central Helsinki."
I wonder how the "grammar-nazis" would analyze this sentence..??.... However the part that I'm wondering most about is ...ydinvoiman vastaiseen kynttilämielenosoitukseen . It seems to be a bit too "overt" for an existential sentence ...Maybe there is another way to say this...???

This last sentence is fairly easy:
Ympäristöjärjestöjen tapahtumassa muistettiin Japanin luonnonkatastrofin uhreja.
...this sentence is a Finnish "passive" /impersonal....the verb, muistettiin = "... remembered..."
So:
"In the environmental movement's event were remembered the victims of Japan's natural disaster."
[Edit:...More typical English:
"Victims of Japan's natural disaster were remembered [ or, memorialized...or, honoured, etc.] ... at the enivronmental movement's event."]