Answer: ORS 90.485 specifically allows landlords to have a vehicle towed if it: (a) Blocks or prevents access by emergency vehicles; (b) Blocks or prevents entry to the premises; (c) Violates a prominently posted parking prohibition; (d) Blocks or is unlawfully parked in a space reserved for persons with disabilities; (e) Is parked in an area not intended for motor vehicles including, but not limited to, sidewalks, lawns and landscaping; (f) Is parked in a space reserved for tenants but is not assigned to a tenant and does not display a parking tag or other device; or, (g) Is parked in a specific space assigned to a tenant (but only with the tenant's agreement at the time of the tow).
First and foremost, you should ensure that you have the proper signage in your park specifying whether and/or when parking is allowed in certain areas (i.e., "No Overnight Street Parking"). Also contact a local towing company to have them post towing company signs around the park.
When you have an illegally parked vehicle towed, the towing company is responsible for taking a photo of the vehicle and reporting to the police that it has been towed. After the car is removed, the towing company takes responsibility for the vehicle and returning it to the owner (after paying the tow fees, of course).
I would also suggest a rule allowing the park to assess parking violation charges of $50 per violation. As required by ORS 90.302 (3), the rule should specify that the first violation would result in a written warning, with subsequent violations within one year being assessed the $50 charge. ORS 90.302 (3) specifies the language that must be included in the written warning, which you should consult with an attorney to draft.
There are certain technical nuances to these statutes, so as usual consult with an experienced attorney before implementing a parking enforcement plan. But the bottom line is that you do have tools at your disposal to cut down on parking problems.