I dug around and put the pieces together to solve the problem myself. Here's how to position an image or element anywhere you want in WordPress: (example: I did this for the bracelet image, which looked like this at the time of this writing: http://www.thefreedomskater.com/wp-content/uploads/2011/03/bracelet_image_location.jpg.
Things you need to know/do:
1) style.css controls everything. Find it in in the WP dashboard under the following path: Appearance>editor
2) The best place to put a random image that will show-up on all pages is in the sidebar/widget bar as an arbitrary text widget.
3) In style.css, make a new CSS ID, which will define the position of the object. It should be set to position:relative; because that allows you to move the image relative to where it would otherwise be automatically placed in the text widget. You can adjust it based on its top and left edges. Here's my example from the bracelet:
img#braceletposition
{
position:relative;
top:-1596px;
left:172px;
z-index:15000;
}
*notes: 1) "img" says that I'm styling an image elment, "#" says that I'm making a specific ID (good for one-offs), and the text afterward is simply what I want to call it. 2) z-index of 15000 is arbitrary and high. It only ensures that the image will be above anything within the stacking context of the sidebar (containing element).
4) In style.css Adjust the z-index of the containing element (sidebar in our case) so that it is higher than anything you want the image to be over. I just did a search for "sidebar" to find it in the sheet and adjusted the "z-index" value to 20000, so it would be sure to be above all menus and other content.
5) Often, containers, such as our sidebar, are set to hide or cut-off objects that overflow past their borders. Since we probably want to move our image outside of the container (as with our bracelet in the sidebar text widget), we need to change this. Again in style.css, we find the sidebar styling information and adjust the overflow command to read: overflow:visible;.
6) When we write our text widget, we'll just make an image tag and call on the id that we defined. in our case:
<img src="imageURLhere" id="braceletposition"/>
7) Of course, we can add links or any other number of modifiers, but this is the basic image, and we can move it as we please by adjusting the values for "left" and "top" within the ID we made in style.css.
Hope that helps some people. I know I've had this problem on multiple occasions, but I think this solution should work in most themes.