Keaja,
The find method includes an :order_by parameter. Just try:
@type_2 = Type2.find(:all, :conditions => {:user_id => @user_id}, :order_by => "created_at ASC")
Actually, it looks like you want to order the whole collection.
Well, you already have the whole list in the last line, so just tack on a ".reverse" and you are all set. I.e.
@types = (@type_1 + @type_2 + @type_3 + @type_4).sort_by(&:created_at).reverse
-Danimal