JR - your first input to the imresize function is the handle to the axes1 object and isn't an image which is required by the re-sizing function. In order to get around this, you can try the following - save the image to the handles structure (whenever you load it), do the resize on this image, and then show the resized image in the axes.
Suppose that you load the image in the OpeningFcn of your GUI. You could do something like
function myGui_OpeningFcn(hObject, eventdata, handles, varargin)
handles.output = hObject;
% load the image
myImg = imread('someImg.jpg');
% display the image in the axes
image(myImg,'Parent',handles.axes1);
% add the image to the handles structure
handles.myImg = myImg;
% update the handles structure
guidata(hObject, handles);
Now, in your callback that does the resizing, just do this
% resize the image
AdjustedImage = imresize(handles.myImg,[ImageHeight,ImageWidth]);
% show the image in the axes
image(AdjustedImage,'Parent',handles.axes1);
In the above I used image rather than imshow because I don't have the Image Processing Toolbox, so you can use whichever is convenient. Try implementing the above and see what happens!