In his final days as president-for-life of Uganda, Idi Amin was a man on the run-racing about eastern Uganda in his red TR7 sports car, one step ahead of the advancing Tanzanian Army.

As his successor, Yusufu Lule, took the oath of office as president today and appealed to the citizens of Uganda to "help me erase the traces of eight years of Idi Amin," the first clear picture of the last 10 days of the bizarre dictator began to emerge.

The final chapter of the Amin saga began April 2 in the town of Entebbe, where Amin spent the night at the State Lodge, a huge whitewashed villa overlooking Lake Victoria.

For this man-child who was both continually seeking pleasure and fearing for his life, the lodge was a wonderful playground as well as a military arsenal.

Its several dozen rooms were filled with every imaginable electronic gadget, sports equipment and adult toy, ranging from movie cameras and tape decks to wind-up plastic boats and board games.

The kitchen was loaded with imported foods and liquors, all unavailable in shops, while the dining room's furnishings included fine china and glasses, silver goblets and serving utensils and long stately tables.

The half dozen or more bedrooms included one filled with cribs and several beds, evidently for his wives and children. In one dresser drawer there was a handmade card reading "Mery (sic) Christmas Daddy and Mummy, your loving son Araba"-a rather strange gift for Amin's son to give his fanatically Moslem father.

Another enormous bedroom, perhaps for one of Amin's several mistresses, contained a huge stuffed teddy bear and doctor's reports on several women.

Piled in the corners of all these rooms were caches of arms and ammunition. These included dozens of automatic weapons of various makes and one 33-caliber hunting rifle equiped with telescope sight and silencer, appartently designed for assassination.

Amin's bedroom contained an armscache, hundreds of confidential intelligence files and a large stock of pornographic magazines.

Amin apparently left Entebbe on Wednesday, April 4, the day the Libyan soldiers and about 50 Palestinian bodyguards and Mig pilots began leaving Uganda. Thursday the Tanzanaian Army occupied the town and by Friday Tanzanian military officers were sleeping in the Entebbe house.

On Friday Amin visited Kampala. In an impromptu radio broadcast he appealed to his soldiers not to desert the Army and promised to mount a strong counteroffensive. He also presented what he said was a Tanzanian prisoner captured in the war.

Later that day, Amin, accompanied by only a few bodyguards, said to be from Zaire and Burundi, reportedly visited a market place near Makerere University, where Moslems usually gather in the eveining. Here Admin, using a loudspeaker attached to his car, informally addressed the crowd, saying the situation was under control.

The next morning Amin in his red sports car-flanked by a half dozen carloads of bodyguards-was seen coming from the direction of Tororo in eastern Uganda. "My guess is he'd been up in Soroti, where he organized to make radio broadcasts," a diplomatic source said.

Since then Amin has made several broadcasts claiming he was in the Kampala studio. Radio employes however, deny that he had been there. Various sources speculate he has been using the Soroti station or the mobile transmitters fitted into several of his cars.

On Sunday, Monday and early Tuesday, just hours before the anti-Amin forces occupied Kampala, Amin is said to have been on the outskirts of the city. Sunday night he reportedly slept at Gaba, about three miles outside Kampala, in a house formerly owned by one of the 50,000 Asians Amin expelled from Uganda in 1972. Amin is said to have taken over dozens of such private houses around the country.

Monday, the night of the heaviest shelling of the capital, the Ugandan dictator reportedly stayed at a friend's house in the Ntinda housing estate just inside the city limits.

There are some reports that he was in Kampala Tuesday morning. Buy by late afternoon he had traveled to Jinja, 80 miles to the east, where he reportedly immediately sent a bodyguard to the local hospital for medicines.

That night, as Kampala fell into the hands of enemy forces, Amin is said to have stayed at the Kyumboyo teachers college, three miles outside the city on the road to Jinja. At the college, Amin reportedly berated several hundred soldiers who had fled the capital for running away, and ordered to them to stay and fight, pledging that a new defense line had been drawn at that point.

Since then, unconfirmed reports say Amin has been staying in Jinja, where he sleeps, either at the military barracks or in the house of his uncle.

Amin has promised to make a final stand in Jinja.

Tanzanian military sources say Tanzanian troops have had small encounters with Ugandan forces about 20 miles outside Kampala along the Jinja road. These sources say the Ugandans have only two tanks, some armored personnel carriers and probably no more than several hundred troops.

Military sources say anti-Amin commandos have now been dispatched to try to capture Amin alive. They say the new Ugandan government wants to put Amin on trial.

While tracking the Ugandan dictator's erratic movements may prove difficult, the anti-Amin forces are confident he will be captured before long. CAPTION: Picture, Yusufu Lule, former college professor, taking the oath of office as Uganda's new president yesterday. AP