CHICAGO, April 21 (Reuters) - U.S. corn and soybean futures climbed to multi-year highs on Wednesday, supported by firm cash markets as old-crop supplies dwindle and weather issues threaten prospects for the 2021 harvests, analysts said.

Wheat futures also rose, drawing additional support from frosty temperatures in the Plains and Midwest.

Chicago Board of Trade May corn settled up 19 cents at $6.25-1/2 per bushel after reaching $6.28-1/2, the highest on a continuous chart of the most-active contract since June 2013.

Benchmark CBOT July soybeans ended up 21-3/4 cents at $14.79-1/2 a bushel, while the spot contract reached $14.99-3/4, nearing $15 for the first time since June 2014.

CBOT July wheat settled up 13-3/4 cents at $6.75 a bushel.

Nearby contracts led the gains in corn and soybeans as traders scrambled to exit short, or sold, positions in May futures contracts ahead of the first notice day for deliveries, on April 30. Traders expect few deliveries against May corn and soy futures given firm domestic cash markets, which indicate tight supplies remaining from the 2021 harvest.

"The shorts are having difficulty getting out of the May ahead of first notice day. The farmer is not selling much," said Dan Cekander, president of DC Analysis.

Worries about dry conditions stressing Brazil's second-crop corn added support, as well as freezing temperatures this week across the U.S. midsection. The Commodity Weather Group said temperatures were cold enough to cause "limited" damage to winter wheat in parts of Kansas and Oklahoma.

The cold could also slow the germination of newly seeded corn. The U.S. Department of Agriculture said the U.S. corn crop was 8% planted by Sunday.

"In a season where you need everything to go right, it's not a great start," said Michael Magdovitz, commodity analyst at Rabobank.

Corn may test a resistance at $6.42-1/2 in one or two weeks, a break above which could lead to a gain to $7.21-1/2, Wang Tao, a Reuters analyst for commodities technicals, said.

In a sign of tightening global availability of corn and soy, China's agriculture ministry published guidelines on Wednesday for the reduction of corn and soymeal in pig and poultry feed.

Tensions in related vegetable oil and biodiesel markets added to the strength in soybeans. The CBOT front-month soybean oil contract struck a 10-year high at 60.38 cents per lb.

(Reporting by Julie Ingwersen; Editing by Kirsten Donovan and Peter Cooney)