I will chime in about Lambda Chi Alpha.
From HQ website:
Lambda Chi Alpha Symbols
Coat of Arms
Perhaps the most commonly seen artistry representing Lambda Chi Alpha is our coat of arms, developed (unlike that of most fraternities) after careful study of the rules of heraldry. Designed by Jack Mason of Epsilon Zeta (University of Pennsylvania), our coat of arms displays our three open mottos, translated from top to bottom, “Crescent in the Cross,” “Naught Without Labor,” and “Every Man a Man.” Present are the crucicrescent, the lamp of learning, the clasped hands of brotherhood, and other symbols, as well as the inescutcheon signifying our merger with Theta Kappa Nu (the white rose is our fraternity flower) and the badge of membership below. In the medieval rules of heraldry it would be described as such:
Escutcheon: quarterly 1, vert, a lighten Greek lamp or; 2, or, an open book proper, bearing on its face the letters Chi, Omicron, Alpha Zeta; 3, able, a balance, or; 4, vert, a pair of clasped hands argent, between three mullets in chevron or; over all an inescutcheon argent, lion rampant holding a white rose slipped proper.
Behind the escutcheon a pair of swords in saltire, points downward, argent, pommels, and hilts or. Mantling vert, lined, or.
Encircling the escutcheon a riband purpire, edged argent, bearing the Greek motto Chalepa ta Kala surronded by an olive wreath which bears pendant the badge of the brotherhood.
Below the escutcheon a scroll with the Latin motto
Vir Quisque Vir
Crest: issuant from a crown celestial or, ensigning a gentlemen's helmet proper, a crucicrescent rayonne or, Latin motto
Per Crucam Crescens, on scroll.
The Badge
Our membership badge is made with the lambda being struck separately from a single piece comprising the chi, alpha, and crescent. The background for the letters delta and pi is enameled, and the lambda is joined to the remainder of the badge (always yellow, white, or green gold) before the eight crescent pearls and (optional) stones in the lambda are set.
The centrality of the badge is a custom continued from our fraternal predecessor literary societies. The Badge is properly worn over the heart, preferably with a badge guard bearing a monogram of the member’s zeta designation, and only by initiated members, their wives, and their fiancees (special exceptions may be made for some housemothers).
Sid note: Delta Pi used to be Delta Phi at the very beginning. It was later changed to Delta Pi in 1912 due to a Delta Phi fraternity on campus.
Associate Member Pin
The associate member pin has a most interesting history because it embodies the official badge of Theta Kappa Nu as well as the original new member pin of Lambda Chi Alpha. The original Lambda Chi Alpha pin was a gothic arch, and with the union, this was superimposed upon the triangles composing the official badge of Theta Kappa Nu.
The Seal
The seal is used to identify official General Fraternity documents and publications. It should not be used for decoration, as an ornament for jewelry, stationery, etc., unless it is to be used as the official stationery for the General Fraternity. It is now properly used on charters, membership certificates, and authorized publications of the General Fraternities.
The Flag
The Lambda Chi Alpha flag may be flown on appropriate occasions or placed on a wall. Chapters may place their Zeta letters in the upper right corner to identify their flags.
The Recognition Button
Unlike many fraternity recognition buttons, that of Lambda Chi Alpha is neither a miniture coat of arms nor a display of the cutout letters. It is a special design showing the cross and crescent combined. It is worn only on the left lapel of a suit jacket or sports jacket. Its original purpose was to permit members unknown to each other to recognize the common bond when the badge was not worn or was obscured by the jacket without "boasting to the world" of one's fraternal ties.
The Friendship Pin
The cross and crescent with shield bearing the Greek letters pin was originally designed to be worn by girlfriends of members when the relationship had not yet reached the state of engagement or marriage. Today, the pin also is worn by members who have not purchased a badge, or by members who prefer its design.
The Flower
The Fraternity flower is the white rose.
The Mascot
The Rampant lion holding our flower, the White Rose, symbolizes "Strength Protecting Innocence".