For subtitle edition/translation (text-based subtitles, that is), I strongly suggest Gaupol.

sudo apt-get install gaupol

Besides of gaupol, you can also try Subtitle Editor and Gnome Subtitles.

However, from the screenshots, it is clear that your .srt file is not encoded in Unicode.

As it turns out, iconv does change the encoding of the file to UTF-8, but the converted file will still have the same characters you see when opening in Gedit.

The solution I found is this:

1. Open Gaupol and go to menu File → Open or click on the button Open.
2. There is a selection menu in the lower part of the open window, titled Character encoding. Click onOther… (last option).

   

3. Select an appropriate encoding for your file, e.g. Greek ISO-8859-7, and click on the button Accept.

   

4. Now open your .srt file and make sure all characters are correctly rendered. Otherwise, repeat the above procedure with another encoding. You can run the command file -bi yourfile.srt to determine the correct encoding of your file (although I’ve read the results are not necessarily exact).
5. With your subtitle file open in the correct character encoding, now go to the menu File → Save as…and change the character encoding option (again, at the bottom of the window) to UTF-8 and save the file (possibly with a new name, for safety).

From: http://askubuntu.com/questions/277565/how-can-i-change-the-encoding-of-a-subtitle-file