* Soybeans rally, testing key moving average

* Corn climbs ahead of Friday U.S. grain inventory report

* Wheat falls, eyeing Black Sea supply

Sept 27 (Reuters) - Chicago soybean and corn futures rose on Wednesday as contracts tested key technical levels and funds adjusted positions in the run-up to closely watched U.S. grains stock data later this week, traders said.

The most-active soybean contract on the Chicago Board of Trade (CBOT) was up at $13.06-1/4 a bushel at 11:00 a.m. CDT (1600 GMT), on track for a fourth straight session of gains after hitting their lowest in more than six weeks at the start of the week.

"It's a little bit of a technical trade," said Joe Davis, director of commodity sales at Futures International in Chicago.

Davis noted that soybean prices are back above "the psychological $13 level," and that on Wednesday the November soybean contract had crossed at one point above its 100-day moving average at $13.06-1/2, a level seen as broadly supportive of prices, before retreating.

"That's positive and that's going to attract further technical buying," he said.

Corn was also up about 1% at $4.84-1/4 a bushel, hitting the highest levels since Sept. 12.

Davis said some traders were adjusting positions ahead of a U.S. Department of Agriculture report due out on Friday on domestic grain stockpiles, betting it could show a drop in corn stocks from USDA's last monthly supply/demand report on Sept. 12.

"There's still quite a few bears out there," he said. "But with the stocks going down and a little bit of a bounce all around, people are taking a shot at buying it."

CBOT wheat fell 1.3% to $5.81 a bushel as signs of ample Black Sea supplies offset concerns about war disrupting Ukrainian shipments and an unofficial export floor price being used in Russia.

Wheat and other crop markets were nonetheless being underpinned by concern that dry weather will curb upcoming crops, notably in the Southern Hemisphere. (Reporting by Zachary Goelman in New York City; Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Richard Chang)