Happy New Year! --这个不用解释了，起头语！
Abundance year after year! --It means to have something left over, for example: grains, or farm goods that kept in your stores are plentiful for the next year. In modern-day times, it means to have something left in your bank account.
Recieve wealth and fortune in abundance! --You're wishing people to have loads of source of income, or in other words, "money to come in from a wide range of sources".
On the up and up! --May every step you take become higher, raise you up! For instance, someone in your family is in a job where they can get a promotion.
May all the wishes come ture! --It's a catch-all-phrase, It means to wish someone achieve whatever they're dreamed about!
To have fortunes reversed! --If someone's been having a bit of a tough year and you really hope that this new year will bring them something different. This is a bit of a harder one，but I think it's really worth learning, becuase you're hoping that their luck will take a turn this year, and showing that you're truly cared about them.
May all your hopes be fullfilled! --To wish people to have everything they desire in all aspects of life. or in other words, "May everything goes the way they wish for".
Good health! --Chairman Mao once said "health is the foundation of revolution", without health, you don't have the capacity to create fortune or enjoy wealth.
Hand over the red envelope! --The final one is not an expression per say, but a very important phrase that usually adopted as joke between intimate friends after greeting each other。