Try AirBnB. Contact the hosts and ask about long term stays.
Some hotels also offer monthly rates, but you'll have to ask around. Try the lower tier hotels just off the main roads.
Here are a few near me in On Nut you can try: Kokotel Bangkok Sukhumvit 50, Cross Vibe Bangkok Sukhumvit, HOP INN Bangkok Onnut Station, Golden House Apartment, Solo Express Sukhumvit 81, KV Mansion, iPREMIUM Sukhumvit 81
Also look for "serviced apartments". They are more likely to do monthly