Object oriented architecture with an image processing code
Reducing repetition

self.sizes

self.sizes being repeated 4 times is not necessary:

    self.sizes                    = OrderedDict()
    self.sizes['image_main']      = (800, 800)
    self.sizes['thumbsize_big']   = (200, 200)
    self.sizes['thumbsize_small'] = (100, 100)


You may give an initial argument to OrderedDict to avoid it:

    self.sizes = OrderedDict( (
        ('image_main', (800, 800)),
        ('thumbsize_big', (200, 200)),
        ('thumbsize_small', (100, 100)) 
    ))


myimage

def resize_image(self, image, size):
    myimage = Image.open(image)
    myimage = myimage.resize(size, Image.ANTIALIAS)
    return myimage


In fact the myimage variable may be avoided completely, just chaining the method calls is much simpler:

def resize_image(self, image, size):
    return Image.open(image).resize(size, Image.ANTIALIAS)


Whole block repetition

        if self.image_format == 'png':
            # Save images on disk
            self.save_image(self.resize_image(self.image, value),save_dir, self.png_compress, self.jpg_compress)
            # Save images in fields
            if self.has_iterated == 0: self.instance.image_main = self.saving_path + self.slug + '_' + key + '.png'
            if self.has_iterated == 1: self.instance.image_thumbsize_big = self.saving_path + self.slug + '_' + key + '.png'
            if self.has_iterated == 2: self.instance.image_thumbsize_small = self.saving_path + self.slug + '_' + key + '.png'
            self.has_iterated += 1
        if self.image_format == 'jpg' or 'jpeg':
            self.save_image(self.resize_image(self.image, value),save_dir, self.png_compress, self.jpg_compress)
            if self.has_iterated == 0: self.instance.image_main = self.saving_path + self.slug + '_' + key + '.jpg'
            if self.has_iterated == 1: self.instance.image_thumbsize_big = self.saving_path + self.slug + '_' + key + '.jpg'
            if self.has_iterated == 2: self.instance.image_thumbsize_small = self.saving_path + self.slug + '_' + key + '.jpg'
            self.has_iterated += 1


The blocks are very similar just the file-extension changes.

extension = 'png' if self.image_format == 'png' else 'jpg'


And then you can delete the conditional branches that follow and leave only one path.

Bug on the use of or

    if self.image_format == 'jpg' or 'jpeg':


Does not work as you intended. or returns the first truthy value, so you wrote the same as:

    if self.image_format == 'jpg':