What is the easiest tool and way to make moving animations that can be used in iOS games? If there are tutorials, I can also learn. I also want it to be vector or retina. Something like hd. Thanks.
That is the key bit of info we needed!
Looking at their documentation for animations it looks like animation is handled within the app--meaning that you create the individual animations yourself outside, then import them as individual frames.
As such, it appears that the tool you need is a drawing tool to create said frames. What is 'easiest' is perhaps subjective, but some options that would fit your 'vector style' requirement would be Adobe Illustrator (commercial) or Inkscape (open source).
Both are vector illustration tools that will give you the style you are looking for that you can then use to create the individual frames for importing into Stencyl.
Either of these tools could be all inclusive for this question and the one you asked about general graphics
Either way, with Illustrator and Photoshop also included, you should get yourself a subscription to Adobe Creative Cloud. You could also use After Effects (in CC too) if you are outputting the animations to video files.