Bill McNulty made a couple stops in the majors with the Oakland team in the late sixties and early seventies...but he was a frequent flier when it came to transactions. His Baseball reference page, however, only lists his draft, a 1972 trade to the Rangers, and a trade to the Mets.
The book "One Hit Wonders" by George Rose goes more in-depth into the slugger's dealings here,
It mentions a trade of McNulty to the Brewers in the offseason before 1971, and the A's buying him back before the season started.
The Cubs are said to have "purchased" McNulty after the 1971 season, and they sent him to Evansville (strangely, the Brewers AAA team). They "gave" him back to Iowa after the season.
Finally, the book mentions that McNulty wanted to play for his hometown club in Sacramento, a new team and an affiliate of the Brewers. It has the Mets and Brewers "able to make a deal" for McNulty to head home.
So, it looks like possible FIVE transactions not documented for Mr. McNulty. Time to go to work!
UPDATE! From the Oct. 24, 1970 Gettysburg Times:
"Milwaukee also traded left-handed pitcher Gary Timberlake to Oakland for third baseman Bill McNulty"
That takes care of one of the unknown transactions, can you help with the rest?