["The Bum Blockade: Los Angeles and the Great Depression” by Hailey Giczy] (http://journals.chapman.edu/ojs/index.php/VocesNovae/article/view/20/94) is a fascinating read. The basics: In February 1936, the LAPD sent 136 officers to man 16 checkpoints along the state’s borders with Oregon, Nevada, and Arizona to stop the influx of migrants. In April 1936, LAPD Police Chief James E. Davis recalled the officers. Giczy suggests it wasn’t the threat of reprisals by the governors of the bordering states, or the ACLU’s maneuvering to bring a lawsuit, but plain old lack of funding that spelled the end of the Bum Blockade.
The officers searched vehicles and trains. Railroads obligingly stopped to allow their freight cars to be searched; migrants could be arrested for fare evasion. But people on the highways were just turned back if the LAPD officers thought they were vagrants.
You can watch newsreel footage of migrants being turned back at https://www.youtube.com/watch?v=zIZDMtRDCxI
While that newsreel calls it “the first state blockade of its kind ever attempted,” Giczy makes reference to a similar program attempted (and quickly scrapped) by Florida.
Giczy also touches on some of the legal wrangling over whether the state of California had the power to turn back transients. It’s well worth a read.
See also http://newdeal.feri.org/tolan/tol09.htm https://www.newspapers.com/clip/7907297/los_angeles_bum_blockade_brings/ http://www.legendsofamerica.com/ca-bumblockade.html
The freedom of U.S. citizens to travel freely among the states was a well-established constitutional right during the Dust Bowl. About 100 years earlier, Corfield v. Coryell (1823) drew the fundamental right to travel out of the Privileges and Immunities Clause of Article IV of the U.S. Constitution.
"The inquiry is, what are the privileges and immunities of citizens in the several states? . . . What these fundamental principles are, it would perhaps be more tedious than difficult to enumerate . . . . The right of a citizen of one state to pass through, or to reside in any other state, for purposes of trade, agriculture, professional pursuits, or otherwise."
Nevertheless, California passed an "anti-Okie" statute in 1937. "Every person, firm or corporation or officer or agent thereof that brings or assists in bringing into the State any indigent person who is not a resident of the State, knowing him to be an indigent person, is guilty of a misdemeanor." Cal. Welfare and Institutions Code § 2615.^1 The Grapes of Wrath was published in 1939 but drawn from articles Steinbeck published in 1936,^2 so theoretically, the checkpoints operating in the book were operating outside of the ambit of the statute.
Almost immediately (but after the book was published), the U.S. Supreme Court found this "anti-Okie" statute to be unconstitutional. Edwards v. California (1941). "It is frequently the case that a State might gain a momentary respite from the pressure of events by the simple expedient of shutting its gates to the outside world. But, in the words of Mr. Justice Cardozo:. . . . '[The Constitution] was framed upon the theory that the peoples of the several States must sink or swim together, and that, in the long run, prosperity and salvation are in union, and not division.'" (quoting Baldwin v. Seelig).
The opinion used the Dormant Commerce Clause, and the Concurrence used the Privileges and Immunities Clause. But really, later we find out that you could use four or five difference places in the Constitution to protect the right of interstate travel. Shapiro v. Thompson (1969).
The second part of your question asks about showing ID. That isn't explicit in California's statute in question. Legally, I haven't found any contemporary ruling that determines if you had to show ID to move among states. That question was answered in 2006 (re: requiring ID to fly), which is beyond the scope of of this sub. Gilmore v. Gonzales (9th Cir. 2006).
^(1. But in Edwards, discussed below, the Attorney General of California seemed to think "that statutes similar, though not identical, to it have been in effect in California since 1860.")
^(2. Correct me if there is an explicit date in the book to set the year).
Edit: removed unnecessary first sentence introduction.
By the way, I mentioned the 1970-ish Guns & Ammo article, "The Return Of The Law Gun." It was about Boulder City Police Chief Bud Bodell, and his revolver which was stolen in the 1930's and returned to him about 1968. I cannot find the article in G & A Magazine on the Internet, so I do not know the exact month it was published. Bodell is the source for the story about all the jobless guys hanging around Boulder City.
Here is an article I found where Bodell's name is mentioned though.
https://www.usbr.gov/lc/hooverdam/police/history.html
I found this also.