what international law(s) are at play here?
In the case of Assange being removed from the Ecuadorian embassy with the consent of the ambassador -- only the Vienna Convention on Diplomatic Relations.
Subsequent likely proceedings are not covered in this answer but, for example, the Universal Decaration on Human Rights can apply to extradition proceedings.
Refugee vs Asylum seeker
The parts of international law that I have read (few) mostly seem to cover refugees. I suspect that most of us use these terms to mean more or less the same thing. There may be a subtle distinction in law that I don't know about (unsurprisingly)
However, there is a significant difference between withdrawing asylum in an embassy and expulsion from a country of refuge. Most International law seems to cover the latter.
Definition of refugee
At the beginning of the 1951 Convention Relating to the Status of Refugees it defines refugee. It does so by referring to older documents. Consequently I don't have a good grasp of how exactly one qualifies and what exceptions may exist.
We can all be reasonably certain that someone fleeing war in Syria and crossing into Turkey should be regarded as a refugee in international law. Assange's case is not so clear.
Citizenship and Asylum
Prior to 2017 Assange was an Australian citizen in the United Kingdom seeking Asylum in the embassy of Ecuador against possible extradition to Sweden because he feared extradition to the United States where he expected to be mistreated.
As phoog commented, in 2017 Assange obtained Ecuadorian citizenship. International laws do not provide for people to be an international refugee in their own country -- or at least that is not usually seen as an international matter. If Assange was an Ecuadorian citizen in Ecuadorian territory, the rest of this answer would not apply. I believe when you obtain citizenship in your country of refuge, you are now a citizen, not an international refugee.
Embassies and Territory
As the New York Times reports
As a matter of international law, an embassy is not ''territory'' of the sending state; it is territory of the receiving state that is accorded, through various treaties and customs, some immunities from host-country law.
This is important because someone being expelled from the London embassy of Ecuador is not being expelled from Ecuador.
Can the mere act of withdrawing asylum really be illegal?
International law on asylum applies where someone outside their home country applies for asylum in the country where they are present.
Some international laws do cover the situation where asylum or refugee-status is withdrawn or where someone is expelled from a country.
Generally a country "shall not expel a refugee lawfully in their territory save on grounds of national security or public order".
Note that, with respect to Ecuador, Assange was not in their territory. lawfully or otherwise.
We can look at some International law, along with other reasons why they likely don't apply to Assange.
1928 Convention on Asylum
The 1928 Convention on Asylum was signed by Ecuador. The UK is not a signatory for geographical reasons so it does not apply to the UK nor to UK territory.
Signed in Havana, February 20, 1928, at the Sixth International Conference of
It is not permissible for States to grant asylum in legations, warships, military
camps or military aircraft, to persons accused or condemned for common crimes,
or to deserters from the army or navy.
Persons accused of or condemned for common crimes taking refuge in any of the
places mentioned in the preceding paragraph, shall be surrendered upon request
of the local government.
Which suggests someone who is sheltering in a legation should be surrendered if they were accused of the common crime of failure to appear in court after being granted bail.
It doesn't explicitly say anything about withdrawing asylum though.
1951 Convention Relating to the Status of Refugees
I believe this applies to both UK territory and to Ecuadorian territory.
Someone who has committed a serious crime is excluded:
F. The provisions of this Convention shall not apply to any person with
respect to whom there are serious reasons for considering that:
(b) he has committed a serious non-political crime outside the country of
refuge prior to his admission to that country as a refugee;
A crime punishable by a year in prison may be serious enough.
C. This Convention shall cease to apply to any person falling under the
terms of section A if:
(1) He has voluntarily re-availed himself of the protection of the country
of his nationality; or
(2) Having lost his nationality, he has voluntarily re-acquired it; or
(3) He has acquired a new nationality, and enjoys the protection of the
country of his new nationality; or ...
Assange acquired Ecuadorian citizenship in 2017.
Sections 32 and 33 cover expulsion:
1. The Contracting States shall not expel a refugee lawfully in their territory save on grounds of national security or public order.
Of course there is another reason this does not apply to Assange -- he was not in the territory of Ecuador.
Being moved from one part of London to another part of London does not constitute expulsion from a country. Certainly not from Ecuador.
1954 Caracas Convention on Diplomatic Asylum
The UK is not a signatory to this since it is not a member of the Organization of American States. So this does not apply to the UK or to actions on UK territory.
The governments of the Member States of the Organization of American
States, desirous of concluding a Convention on Diplomatic Asylum, have agreed
to the following articles:
Article I. Asylum granted in legations, war vessels, and military camps or
aircraft, to persons being sought for political reasons or for political offenses shall be respected by the territorial State in accordance with the provisions of this Convention.
Article III. It is not lawful to grant asylum to persons who, at the time of
requesting it, are under indictment or on trial for common offenses or have been
convicted by competent regular courts and have not served the respective
sentence, nor to deserters from land, sea, and air forces, save when the acts giving rise to the request for asylum, whatever the case may be, are clearly of a political nature.
At the time of his Asylum request, I believe Assange was indicted for extradition to Sweden on charges of rape. Assange promised the court he would show up in court at the specified date for this matter to be considered.
By not showing up, Assange became guilty of the crime of failure to appear.
Other useful references