How can I modify the "Picture Styles" shortcut gallery in Microsoft Office (Word and Powerpoint, specifically)?

It looks like the short answer is no, Microsoft Word doesn't allow you to create or edit picture styles.

However I did find a very nice work around here, here's a formatted version of what it says:

Microsoft Word 2010 provides no means of creating a style for a picture that you can use to quickly format all of your images in the future. However, you have a workaround involving Quick Parts:

Format an Image

1. Add an image to your document by clicking Insert -> Picture
2. Choose a picture in the dialog box.
3. Click the picture, select the Picture Tools tab, and choose Format.

At this point you can adjust how the text should wrap around the picture, indicate whether the text appears on top of the picture, customize a border for the picture, or what have you.

Once you've applied formatting to your satisfaction:

Create a Quick Part

1. click the image to select it
2. Choose Insert -> Quick Parts -> Save Selection to Quick Part Gallery.
3. Type a name for the image, and choose to save it to the Quick Parts Gallery.
4. Save it in your Building Blocks.dotx file.
5. click OK.

In the future, you can add this formatted image to a file like this:

Apply Quick Part to a new Image

1. Insert -> Quick Parts and click the image.
2. Right-click the image.
3. Choose Change Picture and select the new image.

The new image will appear in the existing border, thus saving you from having to reproduce the border (and other formatting) each and every time you add a picture to your document.

Apparently there is no way to apply formatting on insertion, but there's way easier ways to apply formatting:

1. Insert a picture, format it
2. Insert a new picture
3. Click the first picture
4. Ctrl+Shift+C
5. Click the new image
6. Ctrl+Shift+V

This has similar functionality to the Format Painter tool:

Building off the suggestion by Adam, I came up with a simpler solution if you'd like to use the style on multiple images (which is what I like the Quick Styles gallery for). Follow these instructions from Adam's answer to create a Quick Part with the formatting you'd like:

1. Add an image to your document by clicking Insert > Picture and then choosing a picture in the dialog box.
2. Next, click the picture, select the Picture Tools tab, and choose Format.
3. At this point you can adjust how the text should wrap around the picture, indicate whether the text appears on top of the picture, customize a border for the picture, or what have you.
4. Once you've applied formatting to your satisfaction, click the image to select it and choose Insert > Quick Parts > Save Selection to Quick Part Gallery. Type a name for the image, and choose to save it to the Quick Parts Gallery. Save it in your Building Blocks.dotx file, and click OK.

Instead of inserting the image from Quick Parts and swapping the image with the one you'd like to use for each image in your document, instead,

5. Insert the quickpart image one time.
6. Highlight it, and press Ctrl+Shift+C to copy the formatting.
7. Highlight the image you'd like to apply the style to, and press Ctrl+Shift+V

Formatting pictures in 3 clicks of your Quick Access Toolbar...

I understand this is an old post... but it is still applicable due to Office 365's shortcomings.

This solution is designed to apply your predefined custom picture format on a new image pasted from the clipboard. (But if you're a savvy Office user, which you are because you are reading this, you can tweak this apporach to your preference.)

Once this approach is set up, it only involves 3 clicks on the Quick Access Toolbar to format your pictures. All the clicks take place in a very small area of your screen - much more efficient than navigating through the tabs and options in the ribbons.

INITIAL SETUP PART 1: Defining your Picture Format

1. Insert a picture into your document or email. Format it as to your liking. Select the picture.
2. From the Insert tab, click Quick Parts, and click Save Selection to Quick Part Gallery

INITIAL SETUP PART 2: Config your Toolbar

3. From the Insert tab, click Quick Parts, and right-click your Quick Part

4. Click Add Gallery to Quick Access Toolbar

5. Making sure your picture is selected, click on the Format tab

6. Click on Change Picture, then right-click on From Clipboard

7. Click Add Gallery to Quick Access Toolbar

Now that you are setup, you can format your new pictures in 2 clicks.... In this case, have your picture on your clipboard, ready to be pasted into your document or email.

1. Click the QAT button you added from step 2... your Quick Part gallery will appear; Click on your Quick Part. This adds your predefined formatted picture into your document. Select the picture (I admit I didn't count this as one of the clicks!)
2. Click the QAT button you added in step 7. Voila! Your new image now resides in your document with your custom formatting.