The quickest way to expand your horizons is to listen to all types of music, even if you aren't already familiar with them. While you may not want to directly imitate other genres, you can pick up new ideas to work into your style. Learn popular songs and songs that you like. Learning established songs is a good way to broaden your horizons and pick up on songwriting subtleties you weren't already aware of.
Make time to play music as often as you can. Schedule time during the day where you can focus on your craft. Practice songs you already know, improvise and see what sounds good and learn new chords and notes. Play with other musicians every now and then. You may learn new styles and gain ideas that you can blend with your own. Make an effort to try new styles that you don't normally play. You may wind up perfecting your own interesting take on an established style.
You may have a method of songwriting that you prefer, but you can open up your ability by trying new things. If you usually write the music of a song first, try writing the lyrics first for a change. If you normally write songs through improvisation, switch things up and think of a song in its parts. Try writing a chorus and then working around it to find parts that match.
Writing lyrics can be difficult because you must express your ideas in a relatively small space. Try writing about things that have happened to you and phrase them creatively to avoid being overly obvious. Attempt to relate your experiences and views in a way that is universal so that listeners can identify with you. When singing, make sure to use your own natural voice rather than trying to imitate others. Think of your voice as an instrument to come up with vocal melodies. Try taking a lead part you would play on an instrument and removing it to replace it with your voice.