"Strangers" in the OT are non-Israelites living in the land of Israel. The term is גָּר (gār). Although normally translated as "stranger," Strong's gives its primary definition as "sojourner." They could be remnant Canaanites, but often they were citizens of foreign countries with temporary residence. If one holds to a late date for the composition of Deuteronomy, then they were certainly foreigners. This is probably the best explanation in any case whether one sees Deut. as written at the time of Moses or the time of Josiah.
The statements in the OP should be understood as prophetic warnings, not definite prophecies. This is apparent from 28:15:
If you will not obey the voice of the Lord your God or be careful to
do all his commandments and his statutes which I command you this day,
then all these curses shall come upon you and overtake you.
However, as the text makes it clear that they were many moments in which the statutes were not kept, it is reasonable to think that there should be some evidence of the warnings coming true. An example may be seen in the dominance Syria over Israel during the reign of the wicked king Ahab:
And Ben-ha′dad said to [Ahab], “The cities which my father took from
your father I will restore; and you may establish bazaars for yourself
in Damascus, as my father did in Samar′ia.” And Ahab said, “I will let
you go on these terms.” So he made a covenant with him and let him go. (1 Kings 20)
Here, Ben-hadad is portrayed as clearly having the upper hand. If his agreement with Ahab allowed Israelites to open markets in Damascus then it is more than likely that Sryians would do likewise Samaria and other cities. Thus Syrian citizens would be in a position to fulfill the prophecy. However, other kings of Judah and Israel were also known to have paid tribute to foreign powers. Significant trade with foreign nations dates back to David's cooperation with Hiram of Tyre. (2 Samuel 5:11) Such trade provided opportunities for foreigners to prosper at the expense of native merchants, forcing them to go into debt. Thus the prophecy may have come true several times without notice in the biblical text.
We may presume that there were foreigners residing in both Judah and Israel to conduct trade or acting as royal agents. As Israel and Judah failed to retain God's favor, they would have grown weaker financially, and thus the foreigners residing in their cities would have been able to take advantage of the situation, thus fulfilling the prophecies.