Can my landlord evict me using a hand written notice to vacate?

No. The landlord would need to follow the laws for eviction in Justice Court. First would be a 5-Day Notice to Pay Rent or Quit Premises. You would then be able to respond to the Court within 5 days. If you did so, you would get a hearing. If you did not respond, the landlord would next give another notice that the Constable was going to evict you and change the locks.

Depending on exactly what the notice says and assuming it meets all of the legal requirements, then the answer is yes. However, your landlord will have to file an unlawful detainer (eviction) action against you and get a court order evicting you from the premises.

Hand written is all right so long as it contains the statutorily mandated information.

You have the notice, but he still has to go to court to get the process started, but I believe the hand written notice is sufficient to start the process.

In Washington, the landlord tenant act requires that you be served with a specific notice before you can be evicted. The notice can be a 3-day pay or vacate notice, a 20-day to vacate, or a 10-day notice to comply with the rules or lease. The notice can be hand written so long as it is one of these specific notices. The notice must also be served on you either by specifically handing you a copy, serving someone who resides with you, or after trying these, posts the notice on the door and mails a copy. If you do not respond to the notice, you could get served by a process server with a summons and complaint for unlawful detainer and that may lead to your eviction. Whether it is hand written or typed out, if you received a notice, you should take it seriously and contact an attorney to determine your options.

In Delaware as long as they abide by the L/T code it can be in writing. But they don't evict, the Court does. He sends you the 5-day notice then files in court.