I am Jewish and I do speak Hebrew. I can tell you the words they inserted for Surfer Girl are the words to the prayer Lecha Dodi ("Come my Beloved" in English). It's the traditional Jewish prayer sung on Friday Nights by Jews all around the world to welcome in Shabbat (the Sabbath).
Here's a good rendition and translation -
http://www.chabad.org/multimedia/media_cdo/aid/265789/jewish/Lcha-Dodi.htm. This link is sung and transliterated in Ashkenazi dialect. Modern Hebrew is based on Sefardic dialect, which is what most Jews speak today. Surfer Girl was sung in Modern Hebrew.
Good Vibrations is sung to the words of Mizmor L'David, another Jewish prayer. The words are as follows: הבו לאדוני בני אלים, הבו לאדוני כבוד ועז ("Havu La'Adonai B'nei Elim, Havu La'Adonai Kavod Va'oz") "Ascribe unto the Lord, O ye sons of might, ascribe unto the Lord glory and strength." הבו לאדוני כבוד שמו, השתחוו לאדוני בהדרת קודש (Havu la'Adonai Kavod Sh'mo, Hishtachavu la'Adonai b'Hadrat Kodesh) "Ascribe unto the Lord the glory due unto His name; worship the Lord in the beauty of holiness."
The English words that follow are referring to the Exodus story - that God shook the wilderness and the nations when he appeared on Mount Sinai.
It is kind of hard to understand what they're saying in Be True to Your Shul. "Shul" is the Yiddish word for Synagogue.
For Fun Fun Fun, they're singing "God is one, so we put it on our doorposts and gates." The words are referring to the ritual of putting up mezuzahs. Mezuzahs are little boxes that are mounted on Jewish homes' doorposts that contain the Shema Prayer from Deuteronomy, where God instructs the Israelites to inscribe the words he's speaking at the moment on their doorposts and gates.