There are a lot of moving parts here, so it's best to break things down a little.

Scott was a slave courtesy of birth to an enslaved woman. While the property of a physician working with the military, he was taken into a free territory (Wisconsin) and a free state (Illinois). This did not, as a matter of fact or law, instantly free him. It's possible that his enslaver broke territorial or federal law by taking him to Wisconsin and keeping him enslaved there for some time, but Scott did not sue for his and his wife's freedom until back in Missouri. Just crossing the line did not end slavery, legally speaking.

Enslavers had customary and formal rights of transit (passing through with enslaved people) and sojourn (staying a while) codified under state law. Taney's opinion didn't change that. Scott's enslaver kept him in Illinois past the cutoff date for a sojourn. If Scott made his freedom suit in Illinois then this would not be a federal case at all and Scott would probably have been freed. Instead he waited until he was back in Missouri.

The Missouri courts had previously freed people in Scott's situation as a matter of interstate comity. If an enslaver took an enslaved person to a free state, it was the enslaver's loss and not a real threat to the security of slavery in Missouri. But come Scott's case, slavery is right up in the center of politics and the court rules that circumstances no longer warrant such an easygoing attitude. The appeals get us to the Supreme Court chamber in the Capitol.

Taney took the chance to write what he considered to be the final resolution of all the problems that the political world had with slavery. The issue, he reasoned, was not slavery but rather that politicians thought they could and should do something about it. The way to fix that was to outlaw the platform of the Republican party, fly in the face of the moderate consensus as to federal authority over the territories, and run over to the extreme proslavery right. Taney himself was not a proslavery ideologue, but he was happy to deliver for them when push came to shove so the practical distinction is minimal and entirely irrelevant from the POV of the enslaved and antislavery whites.

Scott's legal claim to freedom came from the bans on slavery in Illinois and Wisconsin, both of which hail originally from the Northwest Ordinance and were repeated verbatim in the various acts that established them as distinct jurisdictions. That authority comes in turn from Congress's power to govern the territories as it sees fit, which is right there in the Constitution and was widely agreed upon by people across the political spectrum for decades prior and during subsequent battles over slavery like the one that produced the Missouri Compromise.

Taney ruled that Congress did not have the power to pass a slavery ban in the territories, period. This is much more than he needed to do to dispose of the case. He went on to say that black Americans had no rights a white man was bound to respect and never had had such rights, anywhere in the US. (This is about as good a historical claim as it is an egalitarian one.) So Scott didn't even have the right to recourse to the courts to begin with.

Where does that leave us? The antislavery portion of the Northwest Ordinance, various organic acts spun off from it to organize the states established out of that land, the enabling acts that directed them to write state constitutions, etc, are all unconstitutional and consequently null. This doesn't change anything for Illinois, which is a state now and can do as it likes. Taney here specifically ruled on what Congress can do vis-a-vis territories and territories labored under substantial disabilities in exchange for Congress footing much of the bill for getting them running. Once you're not a territory, you can go either way on slavery and it's accepted across the political spectrum. Even in 1860, the Republicans still promise they don't believe in any constitutional right to meddle with slavery inside a state and almost all of them probably meant it. Abolition in the territories is, as you say, illegal.

The status of slavery in the states is unchanged and it remains up to individual states to decide how they want to handle rights of transit and sojourn. Over the course of the nineteenth century there's a trend toward reducing both but enforcement is spotty unless one has a vigilant antislavery community around. Being in a free state does not free an enslaved person, but it could if they overstay the limits. Of course to manage to secure freedom that way either your enslaver needs to play along or one probably needs access to the courts. As a practical matter, black Americans still do have some access to the free state courts. A younger Dred Scott who was taken to Illinois could probably get an Illinois court to free him and secure some kind of protection against being kidnapped back to Missouri.

The story often ends right there, which leaves out another potentially very important case. A Virginian brought some people he enslaved to New York City, on the way to Louisiana Texas. He does plan to relocate with them, so this is a transit situation. A free black man in the city notices that there are some people enslaved and they've been in town for a while, so he convinces them to seek their freedom and white antislavery men get involved for the legal end of things. The New York courts agree that the people are free. The Virginian doesn't agree, but the legal fight is expensive and he wants to get on with his life. The state of Virginia takes over the case, seeking the re-enslavement and rendition of the people in question. Virginia was pursuing that case through appeals, looking forward to seeing Taney in due course, right up into 1860. Then Virginia busied itself with other things.

We don't know how Taney would have ruled; maybe Lemmon v. Virignia would have been a bridge too far. But he had zero problem coloring outside the lines for Dred Scott and issuing an opinion so wide-ranging that the GOP's position was that most of it didn't constitute binding precedent at all. It's reasonable to expect that he would have done similarly and granted something that amounted to an indefinite right of sojourn in free states. If enslavers can take enslaved people to a free state and enslave them there indefinitely, then state laws against slavery are basically moot and there are no free states.