What was the state of the German rail system in 1944?

Reichsbahn operated reasonably well practically until the end of the war

The reasons for this are easy to understand - unlike oil, Germany had an ample supply of coal (Ruhr and Saar region, Kattowitz-Katowice in Poland etc ...). Direct threats for the railway system came only from various partisan groups and from air attacks.

Partisans were a significant threat to the railway system in areas where they operated (Soviet Union, Yugoslavia etc ...) . However, the damage they inflicted was limited (destroying railway tracks, occasionally blowing up railway bridges etc ...) . Germans repaired damage relatively quickly and punishment for local population was severe. Overall, partisan actions against railway system had most impact if they were done in concert with conventional military offensives. One example for this would be the partisan attacks on railway before and during Operation Bagration. Of course, in areas far from front lines and without significant guerilla force railway transport was not endangered by them.

As for air attacks, they could be divided in two categories: strikes by fighter-bombers and attackers, and strikes by medium bombers.

Fighter-bombers and attackers (think the P-47 and the Il-2) did try to interdict trains coming or going from railheads near the frontline. This was not an easy task, as German trains were regularly armed with railway FlaK, and more importantly tended to travel only during the night in areas with heavy enemy air activity. During the day they were dispersed in railway yards, or were hidden in railway tunnels. Railway yards were protected by their own AAA, and railway tunnels were almost indestructible in WW2 (they required precise hits with heavy unguided bombs from low altitude). Also, right until Autumn of 1944 large part of territory under German occupation was simply out of range for fighter-bombers flying relatively low, both in East and West.

Medium bombers (think B-26) were used to attack important railway and marshaling yards, railway hubs and non-moving rolling stock in general. They did fly at altitudes where they could avoid the lighter FlaK (20 mm and 37 mm to an extent) but not the heavier 8.8 cm. Overall, their operations were somewhat successful, but Germans countered them by dispersing rolling stock and concentrating AAA. In general, freight railroad cars were difficult to destroy completely (they are essentially wooden boxes on steel wheels), while locomotives were usually hidden. Worth to mention that Germany actually increased production of locomotives during the war. Finally, medium bombers themselves had limited range and could not strike the whole German held territory until late in the war.

As for your novel, bear in mind that last major transports for Auschwitz were Hungarian Jews and that ended on the 9th or 10th July 1944. After that trains mostly carried goods in and out from nearby factories practically until January 1945 when the Soviet offensive liberated the area. SS personnel would not have much problem traveling using trains, especially during the night.

In August/September 1944, the German rail system was working reasonably well. It was heavily loaded, and sometimes damaged by bombing. However, the Western allies weren't doing much bombing east of Berlin, so there would not have been much interference with routes to Auschwitz. Starting in October, the Western allies began attacking the rail system systematically, which caused it to break down entirely in early 1945.

Source: The Collapse of the German War Economy, 1944-1945: Allied Air Power and the German National Railway, Alfred C. Mierzejewski, 2007.

Could an SS officer get from Auschwitz to Berlin by train in July/August/September 1944?

Yes. Per the many comments to your question they'd repair the rails as they'd get destroyed. Trains might get delayed, but they would arrive. And per John Dallman's answer the rail system only broke down in early 1945 when allies began to attack it systematically.

presumably the disruptions didn't keep them from shipping people TO Auschwitz. Would an officer leaving Auschwitz use a different rail line?

(This being for a fictional journal, I presume you're not very interested in potential outliers.)

To the best of my knowledge, no trains to concentration camps were cancelled owing to track damage. Delayed, I would assume with some regularity; but not cancelled. The reason I write not cancelled is that the nazis would prioritize troop convoys over holocaust trains. They had zero consideration for whoever was in the holocaust trains. Trains arrived 4 days after leaving on average. The longest transport of the war probably illustrates this best. It departed from Corfu in Greece. When the train arrived 18 days later, everyone was dead when they opened the doors.

As to the journey the other way around, bombings or not it only takes a single track to get the traffic going. And as I've just noted above, the holocaust convoy, rather than the SS or whatever else, would have been the one waiting if two trains were traveling in opposite directions.

If you're writing a fictional memoir of a survivor of Auschwitz, you might want to invest 10 hours and watch the soul-wrenching "Shoah" documentary if you want to try to convey the horrors of the time in your fictional journal. You will weep if there is any humanity in you. But do watch it regardless, because there simply is no way you'll be able to credibly capture the acute horror of the death camps without watching those first hand witness accounts or reading a few books to the same effect (if the latter, make sure you read Maus, the Pulitzer prize winning comic book).