Well, basically goto animation, then rotate, you choose which dimension to oscillate, x, y, or z. Then a speed, for testing I recommend a high speed like 80, then check oscillate.
Now you have to choose your angle, most of what th see above is at 20, so it's oscillating by 20 degrees. Then you also have the,option to base this animation on the hard point or not.
Once you have the movement you want, you'll want to adjust the angle of the objects position until it looks right. Worth everything working the way you want, go back to the animation and lower the speed to what you are happy with.
What I'm also doing here is animating the scale of the tentacles by about 20 percent in the Z dimension.