3 models, joining and nested queries

I have 3 models,

    class Host
      ref: string
      address: string,
      name: string
         has_many :rooms, :class_name=>"Room", :foreign_key=>'host_ref'

    Class Room
      ref :string
      host_ref: string
      capacity: integer
         has_many :bookings, :class_name=>"Booking",
         belongs_to :host

You will need a foreign_key spec on the above.

    Class Booking
      ref: string
      room_ref :string
      start_date: date
      end_date: string

Why is end_date a string?

      number_of_guests :integer
         belongs_to :room

You will need a foreign_key spec here also.

Unless you are connecting to a legacy database that you /definitely/
cannot change then do not use unusual names for the keys, and do not
use string types. With Rails your life will be much simpler if you
stick to the Rails conventions.

Here one should be able to see the vacancies against each host.
A person when he enters the start date, end date and number of persons to
book for a room, he must get the list of hosts who have rooms vacant and
number of vacancies. How can I write the query in rails?

If you cannot see how to write the complete query then, for a start,
just do what you can in the query and do the rest in code. Make sure
that your automated tests check out the results and the tests pass.
Then, if necessary, you can refactor the code and queries to make it
more efficient, secure in the knowledge that your tests will show that
it is correct. If you cannot even see how to make a start then the
first thing is to write the requirement in pseudo code (something like
find hosts where ..and ..). Once you can write that down clearly and
unambiguously then you should be well on the way towards the solution.