Is there any hard, definitive, reliable evidence that it were the Soviets who committed the Massacre of Nemmersdorf (incl. crucifixions and nailing people on barn doors)?
Several, primarily German sources (see below) make it look like fake news.
The symbol of what the Germans would experience after the entry of Soviet troops was the massacre of Nemmersdorf which was exploited for propaganda purposes. It became a portent of German fear of the Russians, purposefully exploited by the propaganda minister Goebbels to increase people's endurance.
On October 18th, 1944, the Soviets crossed the German border for the first time and […] went 60 kilometers (37 miles) into German territory. […] On October 21st, 1944, the Red Army reaches the German village Nemmersdorf not far from Königsberg (today Mayakovskoye in the Kaliningrad region) with approximately 700 inhabitants.
On October 23rd, the Wehrmacht recaptures the village.
Nobody knows completely what exactly happened in the 48 hours [between Soviets capturing the city and the Germans re-capturing it]. Historians assume that in two days between 19 and 30 people were killed (among them 13 civilians).
The Nazi regime uses this event as a propaganda opportunity. It sends messengers to the village who bring terrible messages home. Accoring to them, there were 72 deaths, tortures and crucifixions on barns. Most importantly: All women and children were raped.
Another reporter, to the contrary, mentions lootings, 2 rapes and 26 fatalities (shot in the neck).
The "Wochenschau" shows creepy, most likely fake, images of dead women and children, whose skirts have been pulled up and the underwear removed. In the following months Goebbels initiates a pseudo-objective investigation commission. It consists of representatives of occupied or allied states. Its goal is to investigate the crimes of the Red Army. Witnesses of the events in Nemmersdorf are being influenced and put under pressure.
After the war, the massacre of Nemmersdorf remains a rhetoric weapon agains the "red menace" from the East. Rumors of villages being nailed to barn gates or raped by the Red Army, are extended with further scary details such as castrations and crucifixions. At some point it is said that there is only one man among 72 victims, the rest are women and children. Photos made by Goebbels' propaganda people are taken at face value.
Only in the 1990es was it possible to reduce the exaggerations through interviews with eyewitnesses.
We will never know what really happened in autumn 1944.
English Wikipedia says (my emphasis):
Bernhard Fisch […] interviewed many witnesses still alive on both sides (e.g., Soviet General Kuzma Galitsky, former commander of 11th Guards Army) and crossing out faulty memories against each other, he found out some disturbing details: the German army itself was responsible for destroying the strong German defensive position in front of Nemmersdorf, and after the event no attempt had been made to identify the photographed victims by name.
He was able to conclude that liberties were taken with at least some of the photographs, that some victims on the photographs were from other East Prussian villages, and that the notorious crucifixion barn doors were not even in Nemmersdorf. There also was the tight time schedule of witness Joachim Reisch, reducing the Soviet presence at Nemmersdorf to less than four hours of heavy fighting in front of the bridge.
Another writer, Joachim Reisch, claimed to have personally been at the scene of the bridge when the event was supposed to have occurred. He has said that the Soviet Brigade was on the bridge for less than four hours.
German Wikipedia seems to confirm Miriam Gebhardt's thesis:
Photographs of the [Goebbels'] propaganda campaign as well as reports and articles of the Nazi authorities were regarded in the [post-war] German discourse as reliable sources.
Fotografien der Propagandakompanie sowie Berichte und Artikel offizieller NS-Stellen wurden im bundesdeutschen Diskurs als verlässliche Quellen betrachtet.
That page has a list of people killed by the Soviets and this list contains 26 (not 72) people.