Absolute Radio presenter Skinner beat Tim Westwood and Real Radio's Ditchy and Salty to first place in the 'Best Entertainment Programme' category. The judges hailed his output as "the whole package... entertaining and engaging, with laugh-out-loud moments", adding that the comedian was "a natural host".
His colleague Wood, who is better known as a member of The Rolling Stones, triumphed in the 'Music Radio Personality of the Year' category, beating BBC 6 Music's Jarvis Cocker and BBC Radio 1's Chris Moyles.
The panel said: "Ronnie has lived the life of a thousand men and you feel like a child sitting at his feet as he unfolds his rarefied story book and recounts his great adventures."
Former Premier League footballer Robbie Savage, who is now a pundit and presenter on BBC Radio 5 Live, secured the 'Rising Star' award.
He later tweeted a message of thanks which read: "Thank you the #savagemovement @SavageSoldier @RSavageFans and all my followers I couldn't of won it without you! (sic)"
Voted for by members of the public, previous winners of the 'Rising Star' accolade include Cocker, Kerrang! Radio's Henry 'Singing Henry' Evans and former BBC 6 Music presenter George Lamb.
5 Live dominated proceedings as its breakfast team won a Gold Award in the category 'Breakfast Show of the Year' for shows with an audience of 10 million listeners or more. Comedy panel show Fighting Talk was also recognised in the 'Best Sports Programme' category with a Gold Award.
Victoria Derbyshire collected three gongs, picking up a Gold Award for 'Best News and Current Affairs Programme' and Silver Awards in the categories of 'Best Speech Programme' and 'Speech Broadcaster of the Year'.
The 5 Live drivetime team was given a Gold Award for its coverage of the negotiations to form a coalition government in May 2010, and the station's Ryder Cup broadcast was also rewarded with the top prize in the 'Best Live Event Coverage' category.
Danny Baker, who recently returned to the airwaves following treatment for cancer, won the Gold Award for 'Speech Radio Personality of the Year'. The judges described him as "a true original".
Talksport was crowned 'UK Station of the Year' and children's radio station Fun Kids won the prize for 'Digital Station of the Year'.
Radio 1 and 1Xtra presenter Mistajam, who won two awards, wrote on Twitter: "Thank you to the @sonyradioawards judges & the radio academy, to my team at 1Xtra past & present, to the 1Xtra management, to my family for putting up with me playing music ALL THE TIME and finally to all the #OJs for your listenership & support :)
"I'm now gonna celebrate with a good 6 hours sleep!!"
The Radio Academy committee also presented special awards to BBC Radio 1's Annie Nightingale and BBC Radio 4's Jenni Murray in recognition of their respective broadcasting careers.
> In Pictures: Sony Radio Academy Awards 2011
> In Full: Sony Radio Academy Awards 2011