Evictions can take anywhere from 2 weeks to a month depending on the circumstances of your case. Variables include: how busy the courts are, sheriff workloads, what kind of notice the tenant needs and more.
As a landlord, it is important to have a written lease with a tenant because a written lease makes the eviction process quicker. However, a written lease is not necessary in order to evict a tenant.
The eviction process can seem long and arduous, but in terms of "legal speed", it is really quite fast. Evictions are only 2nd to criminal cases in order of priority with the courts.