What is the ruling regarding the white, viscous, odorous fluid that is discharged without lust, and is released upon excessive movement, or waking up, or leaving the house, and does it necessitate Ghusl?

The cure for obsessive thoughts is to disregard them and pay them no mind. The mentioned discharges are natural discharges (vaginal moisture), which are pure according to the preponderant opinion, but they nullify ablution. Therefore, a ritual bath (ghusl) is not required for them; rather, ablution (wudu') is sufficient. Do not perform ghusl unless you are absolutely certain that semen, which necessitates ghusl, has been discharged. If you are doubtful about what has been discharged, you may assign it the ruling you wish.