Jonah, Nahum and Obadiah prophesied against other nations. Why? Those people didn't know God. This would be the same as if some Hindu would tell me that Shiva is angry with me. This would only make me laugh. And similarly, and maybe I understand it wrong, but God uses foreign nations to punish His people. Then He punishes that nation with another nation. Assyrians -- Babylonians -- Medo-Persians –- etc. This doesn't seem logical to me.
What you are describing is a similar problem that the Jews had. They thought that the God of Israel, Isaac and Abraham was a God of the Jews only. They did not understand that to be a true child of Abraham had less to do with who were your parents and more to do with your faith. In Romans 4:16 Paul says, "Therefore, the promise comes by faith, so that it may be by grace and may be guaranteed to all Abraham's offspring—not only to those who are of the law but also to those who are of the faith of Abraham. He is the father of us all."
The Jews had the idea that the focus of the Scriptures was the nation of Israel. God was trying to get them to understand that his focus was not just Israel but all of mankind. That is in part why they crucified Jesus. They saw Jesus as a threat to the nation of Israel and to their control of it. There are even clues that the disciples were having a hard time grasping the concept that Jesus was the plan (see Acts 1:6).
Now, think of it from God's point of view. If His intent is to get all nations to behave (especially the Jews), then He will have dealings with all of them. The Bible is not a catalog of all the things God has ever done, just all of the things that are part of the plan that He wants us to know about. Some of the nations will be so far removed from the idea of who God is that they are not likely to listen. However, some may listen and that is who God aims to convince. The book of Daniel is a wonderful account of that. In Daniel 4, God interacts directly with the king of the Babylonians and refuses to let him out of the experience until he acknowledged that God was the God of all. There is no indication that Nebuchadnezzar became a Jew. God just wanted him to understand who is in charge. The book of Jonah is similar, in that a prophet of Israel is sent to Nineveh and told the city to repent. Jonah was angry that God made him go. He was also angry that they repented. He wanted the God of Israel to only care about Israel, and he wanted Nineveh to be destroyed. Instead we find out that God was concerned for the ignorant of that city. In Jonah 4:11 God says, "But Nineveh has more than a hundred and twenty thousand people who cannot tell their right hand from their left, and many cattle as well. Should I not be concerned about that great city?"
So, in that sense, the God of the Bible is different than the gods of other nations. An Indian may believe that Shiva is angry with us, but that Indian is unlikely to tell us that because the focus of the Hindu god is for Hindus. Non-Hindus are not really of any concern. The God of Abraham is not just concerned with Israel, but with getting all men to come to obedience (II Peter 3:9). We are also unlikely to be concerned with Shiva because Shiva has never worked the kinds of miracles that the God of Israel had. That has always been a problem with the gods of the world. They can be angry, but the most anyone ever subscribes to them is an occasional natural disaster; and even then, it is normally an after-the-fact subscription. False prophets are excellent at telling you why a natural disaster occurred after the fact. The fact still remains that the events that they ascribe to a god or gods are still within the natural order of the world. The God of Israel foretells -- not only for Israel, but other nations as well -- of when they will be victorious and when they will be doomed.
I don't think you have misread the events at all. The Assyrians and the Israelites were being evil. The Israelites knew better. It is hard to say exactly what the Assyrians were, but it would seem that they were evil beyond hope. Therefore, God used the Assyrians to punish Israel in part because Israel was not so far removed from being able to repent. Israel refused to repent, and, therefore, God executed His full judgment on them. Then He wanted the Assyrians and the rest of the world to know that the evil of the Assyrians was not tolerated either. He, therefore, executed His judgment on them. They both deserved what they got. It was just that God chose an order of punishment that left the best possible example for those of us who followed.
The same can be said for all of the events that we see now. God is concerned with the world that we live in just as much as He was concerned back then. If we think about it, there are really three types of people in the world: the righteous, those doing evil but who still are able to repent, and those who have become so calloused as to be beyond repenting. Our job is not to figure out who is in which group. Our job is to figure out which group we are in. Some people try to figure it out by assuming that because God is using them; they, therefore, must be among the righteous. However, God used evil people to get His purposes done. The fact that God is using you to accomplish something is not a good enough reason to relax. He used Pharaoh – and then destroyed him. He used the Assyrians – and then destroyed them. He used Babylon – and then destroyed them. Our only safe method to figure out if we are on His good list is by comparing our life to the description given in the Word of God.