Hiya! This is Eli, of the Eli Hunter Band. Here is some interesting/weird tricks that I use to make my songs sound new. All examples will be given in the key of C unless otherwise stated.
1. Borrow Chords.
Alright, this is probably the most common trick, but it is not without its power. When using "borrow" chords, you are taking chords from related key signatures (The most common being the relative minor and the parallel minor), and using them without totally changing the key. What does this mean? Okay, so say you are in the key of C (obviously, right?). The most common chord for you to use are Bb. Play C, Bb, F, C (The argument could be made that you are functioning modally, but if the rest of your song is in C, you're in C). I could get all theory-tastic, but I'll just say that try using the chord one full step below your tonic. There are plenty of articles that explain why this works, so if you want the whole story, read those.
Example: "Peggy Sue" by Buddy Holly, I think.
2. Minor 7's to 6's.
Okay, Here's a fun one. Take an am7 shape (I use x02213), and go to am6 (x02212). This gives a sullen, bitter jazz feel to your progression. If you wanted to get back to your tonic, you could complete the chromatic scale by going am7, am6, F major, C.
Example: "Happiness Is A Warm Gun" by The Beatles.
3. Modal Changes.
Use sparingly. In the key of C, go F, fm, C. If you want to make the minor extra wrenching, consider adding a six (Tritone Goodness!). Another degree to use this would be in the key of G (for ease and familiarity) to go am G D Amajor. So, either the fourth or the second. Got it? Good.
Example 1: "Creep" by Radiohead.
Example 2: "Little Black Submarines" by The Black Keys.
4. "Jazz" Endings.
This is the practice of not ending your song on a clean tonic chord. The most common is to end on the relative minor (Aeolian Mode, yo). That would be Am in C and Em in G. An interesting ending I've been using for 12 bar blues turnarounds is the parallel minor add major7 of the tonic. I do it in E, like so: 021000. A really shocking ending I've been fiddling with is to go to an Amaj7 (X02120) from Cadd9 (X32033). Finally, you always have ending on the parallel major if you are in a minor key (dm, D major).
Examples: I dunno. Let me know if you find any.
5. Major 7 to Minor 7.
Okay, this one's pretty simple. Take a G power chord (355---) and lower the top note one fret at a time (354---, 353---). Then, go to C or Em or something haha. If you wanted to, you could easily go down an extra half-step or two.
Example: "Meadowlark" by Fleet Foxes.
6. Chord Inversions.
Why wasn't this higher on the list? Okay, take a G chord (320033). Mute the bottom note (X20033) You now have an inversion. Pianists will call them first inversions, or second inversions, but most guitarists would call this G/B ('Cause the B is on Bottom). You can do this with any note of any chord.
Examples: "We Are Young" by Fun.
7. Augmented Chords!
This has been my favorite trick of late. Take a C triad (X320XX), and sharp the fifth (X321XX). A good chord to complete the chromatic slide is am (X02210). This gives a devil-may-care attitude jazz feel to your tune.
Examples: I dunno. "Groove Merchant" maybe? A lot of jazz uses this.
8. 1, 5, b5, 4, 1.
So, I do this one in E. It goes E (022100), B (X24442, or X24440, if you like 11's.) Bb (X13331), A (X02220), E. If you get the slide done in as few beats as possible, you'll get a funk feel out of these chords.
Example: I dunno.
9. Extended. Freaking. Harmonies.
This is one of the best tools, and most underused in any guitarists toolbox (I'm getting sick of power chords). Now, the most common one is the 7, but 9's, 11's, and 13's have a power about them. Now, fancy jazz fingerings are a bother to use, but there are some easy chord groupings with similar shapes. The first one is the family I like to call the "Hurr I Play Guitar Chords". This family has theses chords Cadd9 (X32033), G (320033), Em7 (022033), Dsus4 (XX0233), A7sus4 (X02233), and any other whatnot you choose to use. The common notes are of course, the D and G in the top two strings. The second family is what I like to call the "Flutter" Chords. In this family, we have C (X32013), Am7 (X02213), Fadd9 (XX3213), G11 (320013), and whatever else you want to throw in there. These chords are angsty as hell.
Example 1: "Wonderwall" by Oasis.
Example 2: "Michigan" by The Milk Carton Kids.
This one's pretty simple. Basically, what you do is, you stay on one chord and move the third up and down. My favorite chord to do this on is D (XX0232, unless you tune to drop D and use 000232). Simply play D, then Dsus2, then Dsus4, then D again. You can also do this with dm (XX0231). Also, D5 (XX0235) is a fun variant to use. These chords make for a good bridge, I've found.
Example 1: "You Ain't No Sailor" by Marcus Mumford.
Example 2: "Thistle And Weeds" by Mumford And Sons.
Alright, that's about it. Just some fun simple what-not to make your songs interesting.