In Genesis 38, Judah gives his seal, cord and staff as a sign of his pledge to pay Tamar. What are each of these objects and their significance and what is the significance of the pledge itself?
The answer is simple. These three item are unique to Judah and Tamar wanted them only to prove that Judah was the father of her child (and proving that she did not commit adultery, but had conducted herself through the rules of Leverite marriage). See Sforno's commentary. None of these items had monetary value: the cord (Onkelos HaGer translated this as a "ושמלתך שאתה מתכסה בה" -- a wrap with which you cover yourself; see Rashi's commentary to this verse) is custom-made article of clothing; the staff would be something Judah carved himself; and the signet ring was a stamp used to identify Judah's property.
The distinctiveness of these particular items is that when Tamar is accused of adultery, instead of embarrassing her father-in-law by saying, "you are the father of my unborn child," she says at verse 25 that the owner of those three items is the father -- she has left it up to Judah to admit the truth or stay quiet and let her die by fire. From this Jewish tradition teaches “It is better for a person to be cast into a fiery furnace than to embarrass his fellow in public.” [from Babyl. Talmud, Sotah 10b]
A sweet element to this story is that Judah tries to pay off the "harlot" (Tamar) with a kid (Gen. 38:23). Rashi there points out the irony that Judah tried to deceive his father with the blood of a kid that he poured onto Joseph's coat of many colors, and here he was deceived with a kid.
All three objects signify the distinction of someone in a position of authority. The seal was either an amulet of a ring embedded in clay which left an impression signifying its owner. For examples see: Deu 32:34; Neh 9:38; Neh 10:1; Est 3:12; Son 8:6; Isa 8:16; Jer 22:24; Jer 32:44.
There are multiple meanings for cord in scripture. In the case of Gen 38 I believe it pertains to an object, like a rope, that binds things together. (Jdg 15:13; Psa 2:3; Psa 129:4).
A staff, or rod, can refer to an object that assists walking and shepherding. But typically it refers to power in scripture. One particular passage that comes to mind is Ex. 17:9,11.
Moses said unto Joshua, Choose us out men, and go out, fight with Amalek; tomorrow I will stand on the top of the hill with the rod of God in my hand. And it came to pass, when Moses held up his hand, that Israel prevailed; and when he let down his hand, Amalek prevailed (Exod. 17:9, 11)
As far as the significance of the pledge, the answer may lie in Judah's ignoble gesture to Tamar and the sovereignty of Almighty God.
One can not help notice how the narrative of Judah and Tamar is nestled between the narratives of Joseph's betrayal by his brethren and his entrance in to Egypt. But chapter 38 is of supreme importance because it narrates the continuance of the tribe of Judah, the tribe which the Christ would descend from. Due to the evil deeds by Tamar's first two husbands (Judah's first two sons), the Lord took their lives leaving only one son. Judah's reluctance to give his last son in marriage to Tamar was actually a good thing. Without divine intervention, the line stemming from Judah would have been lost. Keep in mind that Judah's wife was a Canaanite. And just as Abraham instructed Isaac not to marry women of the Canaanites, (Gen 28:1) the twelve tribes were to heed the same command. Although Judah's intent to fornicate with a temple prostitute was sinful, God's sovereignty preserved the line of Judah from Canaanite infusion.
I've not read any scholarly insight regarding the significance of the three objects and Judah's pledge. Yet I think it all rests in what all truly belongs to the true King of Kings.
Psa 23:4 Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou art with me; thy rod and thy staff shall comfort me.
Psa 2:3 "Let us burst their bonds apart and cast away their cords from us."
Rev 7:3 saying, "Do not harm the earth or the sea or the trees, until we have sealed the servants of our God on their foreheads."
The 3 items in Gen 38:10, staff, signet and cord, can be identified in Genesis 49:10 as scepter, lawgiver and between his feet. The staff that departed from Judah in his experience becomes the scepter that will not depart in Jacob's prophecy; the signet becomes the lawgiver or engraver; the twisted cord becomes that which is between his feet - his lineage.
A seal is a stamp of one's identity/association, an endorsement of one's true allegiance.
A cord is a bond of one to another, e.g. an umbilical cord, etc.
A staff is for protection: in ancient Israel a staff was (and still is) used by men from a young age of about 13; they carry it around walking in the village to wave away dogs and stray wild animals, as well as invasive people.
Since we all know that God does everything for a reason, this occurrence by Judah and Tamar show us an importance of a SEAL, CORD and STAFF unity. That is, where there's one's seal, there's a bond created resulting in protection. God's SEAL we know is the SABBATH, how, because all the other pagan and other gods have the commandments similar to Christians ones e.g. do not steal, do not kill, etc. BUT they can never have the SABBATH commandment; it's unique to God Almighty of the Christians, it's God's SEAL of authority to mankind. The message of the SEAL, CORD and STAFF team/unity therefore is that we need to keep the SABBATH and we'll have the BOND with Him leading to PROTECTION/SALVATION. This message ties in with Revelations 1 where Jesus is standing on the 4th candle, the middle or midst of the 7 candles. We all know that the 4th candle is even the highest in the Menorah, we know the 4th commandment says KEEP SABBATH HOLY. Jesus is standing on this 4th candle with judgment feet, i.e. the feet like brass/bronze. We all know its only the Brazen Alter that was overlayed with Brass/Bronze. The brazen alter was where sacrifice to remit judged sin was burnt. Even when Jesus was dying on the cross He shouted "Eli Eli Lelamasabathane" meaning in ancient Hebrew (which is now Bantu language) "This This is for Sabbath Keepers". The pagans mistranslated this line in the Bible deliberately saying it says Father why have you forsaken me, which doesn't even connect to the words, all because they know THE IMPORTANCE OF SABBATH to your salvation. The pagans are now in a process to enforce Sun-Day law to completely wipe out Sabbath... think about this when you're ignoring Sabbath and embracing the Sun worship.