bad, big, devastating, ferocious, fierce, great, heavy, killer (informal, esp. AmE), major, monster (AmE,informal), raging, severe, terrible, tremendous, violent
perfect (figurative, esp. AmE)
The company was hit by a perfect storm of negative conditions that converged on it.

approaching, gathering, impending
the dark clouds of an approaching storm

freak
summer, winter, etc.
tropical
monsoon
electric, electrical, lightning, thunder (usually thunderstorm)
hail, rain, snow, wind (usually hailstorm, etc.)
ice (esp. AmE)
dust, sand (usually sandstorm)
magnetic, solar

be in for
I think we're in for a storm (= going to have one).

brave
She had to brave an ice storm to get to the interview.

shelter from, wait out (esp. AmE)
We tried to find a safe place to wait out the storm.

track (esp. AmE)
We'll be tracking the storm as it makes its way across the Gulf.

hit (sth), strike (sth)
It was the worst storm to hit Sri Lanka this century.
Where were you when the storm struck?

rage
The storm raged all night.

be approaching, be brewing, be coming
A storm had been brewing all day.

blow up (esp. BrE), break
The storm broke while we were on the mountain.

blow in, move in
A storm blew in off the ocean.

move across, over, etc. sth, sweep across, over, etc. sth
A major winter storm is moving across the country today.

batter sth, lash sth, ravage sth, sweep sth
a boat battered by the storm
Winter storms swept the coasts.

abate, blow itself out, blow over, clear, clear up, pass, subside
The storm blew over after a couple of hours.

last
The storm lasted for three days.

cloud (often figurative)
In 1939 the storm clouds gathered over Europe.

surge (esp. AmE), water
We're forecasting 14 to 16 feet of storm surge.

damage
Insurance companies face hefty payouts for storm damage.

warning
a tropical storm warning

door (AmE), drain, window (AmE)

during a/the storm, in a/the storm

at the height of the storm
bear the brunt of the storm, take the brunt of the storm
The east coast of Florida bore the brunt of the storm.

seek shelter from the storm (often figurative), take shelter from the storm
I took shelter from the storm in the clubhouse.

the calm before the storm (figurative)
the eye of the storm (often figurative)

approaching, coming, gathering
a gathering storm of discontent

media, political
fire (usually firestorm)
His comments brought down a firestorm of criticism.

arouse, cause, create, provoke (esp. BrE), raise, spark (esp. BrE), unleash
face
ride out, survive, weather
The government is determined to ride out the political storm caused by its new immigration policy.

blow up, break, erupt (all esp. BrE)
A storm blew up between Britain and the US over Venezuela.

blow over, pass
The political storm had blown over at last.

amid a/the storm (esp. BrE)
The band toured Ireland amid a storm of controversy.

storm between
storm of
His comments created a storm of protest in the media.