Well, I don't particularly want to read the docs for easyhtmlparser, but if you're willing to use Beautiful Soup:
from bs4 import BeautifulSoup
fd = open('file.html', 'r')
data = fd.read()
fd.close()
soup = BeautifulSoup(data)
for link in soup.find_all('a'):
print(link.get('href')) #or do whatever with it
should work, but I haven't tested it. Good luck!
Edit: Now I have. It works.
Edit 2: To find an image, search for all the image tags and such, find the src links. I trust you can find how in the Beautiful Soup or easyhtmlparser docs.
To download and put into a folder,
import urllib
urllib.urlretrieve(IMAGE_URL, path_to_folder/imagename)
or you could just read from urllib, since in the end everything is just a string, and read is more straightforward than retrieve.