value_template: >
Alarm {{ states('sensor.alarm_state') }} by {{ states('sensor.alarm_changed_by') }} the {{ states('sensor.alarm_changed_when') }} with a {{ states('sensor.alarm_changed_with') }}.
or
value_template: >
Alarm {{ states.sensor.alarm_state.state }} by {{ states.sensor.alarm_changed_by.state }} the {{ states.sensor.alarm_changed_when.state }} with a {{ states.sensor.alarm_changed_with.state }}.
Things that you were doing wrong:
Accessing state object’s state incorrectly. Use the state method or state object state directly: states('sensor.xxx') or states.sensor.xx.state.
You’re using a multiline template, but treating it like a single line with your quoting. If you want to make a single line template, wrap it in quotes. If you want a multi-line template, use the >.