To be able to upload files from an Android application and use the Multipart content type you need to add some additional jar files to your application. The files needed are apache-mime4j, httpclient, httpcore and httpmime. All are opensource projects built by the Apache foundation. Download the 4 files and add them to your project then you should be able to use the following code to post strings and files to pages.

HttpClient httpclient = new DefaultHttpClient();
HttpPost httppost = new HttpPost("http://www.tumblr.com/api/write");

try {
	MultipartEntity entity = new MultipartEntity();

	entity.addPart("type", new StringBody("photo"));
	entity.addPart("data", new FileBody(image));
	httppost.setEntity(entity);
	HttpResponse response = httpclient.execute(httppost);
} catch (ClientProtocolException e) {
} catch (IOException e) {
}

The image variable in this case is a File that contains an image captured by the camera on the phone.