Chapter 23:
I don't understand why it's okay to eat off your neighbor's land.
Ted: Basically, all of the land of a tribe belonged, in a general sense, to everyone in the tribe. Anyone of that tribe could walk anywhere on the land allotted to the tribe. Also, a person might be hired by a neighbor to help harvest a crop.

While on that land, for quick nourishment, a person could pick any grapes and grain that could be eaten on the fly. But he could not stockpile a bunch of grapes, nor cut down any stalks of grain, to take with him. I suppose that this would have been crossing the line of "stealing" because, presumably, a person had his own grapes and grain back home.

Chapter 24:
Many passages talk about bloodlines being responsible or held accountable (or just detestable, etc) to the 3rd or 4th or 10th generation. What gives?
Ted: All of the latter chapters in Deuteronomy are instructions and commandments for the people who will be going into and claiming the land that has been promised to them. Back in the Ten Commandments, God said, "I, the LORD your God, am a jealous God, punishing the children for the sin of the fathers to the third and fourth generation of those who hate me" (Exodus 20:5). God considered the generations, prior to the one who was about to inherit the new land, as those who "hated" Him. This was exemplified by their constant complaining, rebellion, disobedience, and lack of faith in Him.

Consider Numbers 14, where the people grumbled and griped about entering the new land, because they were afraid of the giant people there. Moses brought up the "third and fourth generation" thing to God (14:18). God said that not one of the people who had treated Him with contempt would ever see the promised land (14:23). He added that even the children of that unfaithful generation would suffer in the desert forty years (14:33).

Then that unfaithful, rebellious generation passed away, and the youngest generation was about to enter the new land. The rules changed somewhat, because this new generation was not unfaithful and disobedient toward God. So no longer would the "children [be] put to death for their fathers; each [was] to die for his own sin" (Deuteronomy 24:16). For further reading, I have written more about generational curses in my online book.

You mentioned the "tenth generation." As far as I can tell, that applied only to descendants of a forbidden marriage and to the descendants of an Ammonite or Moabite. They could not enter the assembly of the Lord, down to the tenth generation (Deuteronomy 23:2,3).

Chapter 25:
25:4 has another seemingly trivial command. Can you draw any connections?
Ted: The only problem I have with this statement, "Do not muzzle an ox while it is treading out the grain" (Deuteronomy 25:4), is that it is not included at the end of the previous chapter (24). I do not know why it was wedged between the section about flogging a guilty man (25:1-3) and a brother's duty to reproduce for his dead brother (25:5-10).

Having said that, the idea of not muzzling an ox while it is treading on the grain (so that it can eat some of the grain and have the energy to continue what it is doing) is one that Paul talked about (1 Corinthians 9:7-14). He pointed out that it was not really oxen about which God was concerned (9:9). Basically, Paul put forth the premise that someone doing God's work was entitled to be supported by those for whom that person was helping by doing the work, just as an ox should be able to eat some of the grain while he was treading it.