I really LOVE your question! I also get into "a very Strawberry mood", a lot!
I even made a website for it, StrawberriesForStrawberryLovers.Com
http://www.strawberries-for-strawberry-lovers.com
And I'm building a special section, just for strawberry music!
http://www.strawberries-for-strawberry-lovers.com/strawberry-music-reviews.html
You'll find links to my reviews of Strawberry Avalanche, Strawberry Fields Forever, Strawberry Letter 23 (the Shuggie Otis, The Brothers Johnson, the Tevin Campbell, AND the Quincy Jones w/Akon versions), and Strawberry Swing. They're all classics (or classics to be)!
I also want to recommend some other strawberry songs (I plan to review them, too, when I have time).
The song "(Love Tastes Like) Strawberries" is a nice song. It's an old folk song that Myriam Makeba made famous (it has a slow, kinda 1960-ish sound). Another famous version was made by Jerry Butler (also has a 1960-ish sound... but a bit different than the Makeba version). And more recently, my favorite version was made by jazz musician Hugh Makela (lots of piano, and trumpet... Makela is a trumpeteer).
If you want a REALLY 1960-ish, psychedelic sounding song, "Strawberries Mean Love" by Strawberry Alarm Clock is a favorite of many people.
These songs are very famous, but there are several others that I've discovered that I think are also really great!
For example, if you like an upbeat, slightly punk sound, I would recommend listening to "Strawberries" by Table 21.
The song "Strawberries" by Buzzard Song is also upbeat, but with a very gentle, and a slightly bluesy sound. Just a single male singer and an acoustic guitar, singing about his little daughter in the strawberry patch. :)
"Strawberry" by Kelsey is also a man singing about his daughter, but has a very soulful sound, and is not quite so upbeat.
If you want soulful as well as upbeat, "Strawberry Lemonade" by Darnell Kendricks is highly recommended. Really nice... one of my favorites!
Another song titled "Strawberries" that you might like is by a singer named Alvin Love, off his "The Strawberry Project" album. It's a pop/light rock song, and the lyrics are basically about a man asking the lady to whom he's attracted to compare the sweetness of his love with the sweetness of strawberries. A little quirky, but very cute!
There are LOTS of "strawberry" songs, but unfortunately, many of them aren't all that good. Hopefully this list will save you some time finding really good songs!