Snowing

There were was a lots (lot) of snowing in Tokyo last week.

I heard that it (has not/hasn't) snowed in 14 years.(how do you say after an interval of 14years)(We'd usually has not/hasn't to show after an interval of time) 

Some traffics were damaged . (I don't what you mean by this.) (Do you want to say "It caused traffic." Or "There was traffic" )

Trains and buses were really late.

In (During) the day, I went to hospital by bus but, it was hard to pick up  get a taxi when I went home.

There were was a lot lots of snowing in Tokyo last week. 

I heard that it snowed in 14years. I heard that it hasn't snowed in Tokyo for 14 years (or "I heard that it hasn't snowed for 14 years" if you don't want to say where).

Some traffics vehicles were damaged. (You may be trying to say: "Cars were damaged", or you may be saying that "It caused traffic"

Trains and buses were really late.

During the day, I went to the hospital by bus but it was hard to pick up find/get a taxi when I went home.