I have the following MySQL script which I want to implement in PostgreSQL.
SET @statement = search_address_query;
PREPARE dynquery FROM @statement;
PostgreSQL does not normally use variables in plain SQL. But you can do that, too:
SET foo.test = 'SELECT bar FROM baz';
SELECT current_setting('foo.test');
Read about Customized Options in the manual.
In PostgreSQL 9.1 or earlier you needed to declare custom_variable_classes before you could use that.
However, You cannot EXECUTE dynamic SQL without a PL (procedural language). You would use a DO command for executing ad-hoc statements (but you cannot return data from it). Or use CREATE FUNCTION to create a function that executes dynamic SQL (and can return data in any fashion imaginable).
Be sure to safeguard against SQL injection when using dynamic SQL.
Related question about custom variables:
Is there a way to define a named constant in a PostgreSQL query?