You can insert into a table from a SELECT.
INSERT INTO
Employee (emp_id, emp_name, emp_address, emp_state, emp_position, emp_manager)
SELECT
001,
'John Doe',
'1 River Walk, Green Street',
(SELECT id FROM state WHERE name = 'New York'),
(SELECT id FROM positions WHERE name = 'Sales Executive'),
(SELECT id FROM manager WHERE name = 'Barry Green')
FROM
dual
Or, similarly...
INSERT INTO
Employee (emp_id, emp_name, emp_address, emp_state, emp_position, emp_manager)
SELECT
001,
'John Doe',
'1 River Walk, Green Street',
state.id,
positions.id,
manager.id
FROM
state
CROSS JOIN
positions
CROSS JOIN
manager
WHERE
state.name = 'New York'
AND positions.name = 'Sales Executive'
AND manager.name = 'Barry Green'
Though this one does assume that all the look-ups exist. If, for example, there is no position name 'Sales Executive', nothing would get inserted with this version.