With the invasion of Ukraine, I've heard a few Japanese words used for this action -- 侵攻 and 侵略 among them. I think I've heard 攻撃 as well, although perhaps as a more general term for attack. A dictionary search for invasion suggests a slew of words, including 侵入 and 侵犯. What words are most appropriate, are there meaningful nuances among them, and, if relevant, which are more (or less) likely to be used in everyday conversation?
As for the last question, 攻撃 and 侵入 are ordinary words.
攻撃 is an attack in many contexts. For example the batting side in baseball is called 攻撃側 (lit. attacking side).
侵入 is entering into a place where one is not supposed to, with or without armed forces. So the act of sneaking into a house is 侵入, but can't be a 侵攻 (even if s/he has a gun).
I don't think 侵攻 and 侵略 are clearly distinguished in ordinary speech, but 侵攻 sounds a military advancement into other countries' territory whereas 侵略 sounds an advancement + taking control over the territory. Accordingly, 侵略 sounds worse than 侵攻. (In dictionary terms, 侵略 has 'taking territories and possessions of other countries' as an addition to 侵攻).
According to this, 侵略 is the official translation of aggression as defined by UN. And 侵攻 is the word for invasion. I suppose outside specific contexts aggression and invasion are not that clearly distinguished, and the same is true for 侵略 and 侵攻.
侵犯 is a word used mostly in the context of territorial disputes, meaning an infringement of (territorial) rights. 領域侵犯 means a country entering another country's territory and 領海侵犯 is entering the sea (the word often appears in connection with China). FYI a broader word for infringement of rights is 侵害.
So, at least from the Western viewpoint, Russia's act can be described as either of them depending on the focus: 侵入(entering), 侵攻(entering with the military), 侵略(occupying the territory), or 攻撃(actual bombing etc.)
I think the word '侵略' usually implies negative evaluation by the speaker. In other words, the speaker chooses the word '侵略' intentionally over '侵攻' to include the meaning that there was wrong doing by the occupying forces (e.g., inhumane treatment of civilians). Yet in other words, the listener usually detects that the speaker used the word '侵略' intentionally to add negative evaluation to '侵攻'.
To convince yourself about this point, you may search if Japanese major news papers used the word '侵略' for the US and allied forces entering into Iraq, for example, and it'll be difficult to find such a case. Usually, it is called 'イラク侵攻'. In contrast, you will often find that '侵略' is used for the Japanese occupation of regions in Asia during the Pacific war. Note that not all occupation is called '侵略'. A more neutral word for occupation is '占領'. Occupation of Japan by the allied forces after the war is not usually called '侵略' but '占領'.
For the current Russian invasion of Ukraine, the news papers seem to have used '侵攻' so far.
cf. テーマ ウクライナ侵攻, 日経新聞 https://www.nikkei.com/theme/?dw=22012404