1)

MADELINE HAYES: "This is something, as cheesy as it sounds, that I’ve always dreamed about, that there will be a boys school that doesn’t charge twenty-five thousand dollars a year, but would give the same academics, the same level of interaction and leadership.”

Isto, falso (ou cliché) como posso parecer, é o que sempre sonhei...

Isto, hipócrita como posso parecer (significando que a primeira coisa que virá a cabeça é que todo mundo poderia dizer isso, mas...), é o que sempre sonhei...

Isto, lugar-comum como posso parecer, é o que sempre sonhei...

Isto, contrário ao que muita gente (provavelmente) possa pensar , é o que sempre sonhei...

2.)

I'm a HUGE...HUGE Nigella Lawson fan. Next to Martha, Nigella is my next idol. As cheesy as it sounds, it's true.

Mesma coisa, em termos de ''(isso) pode parecer hipocrisia mas é verdade"/  pode parecer insincero, mas é a pura verdade/ pode parecer fingimento, mas não, é verdade.

Cheesy aqui seria algo como:  Hipócrita/falso/insincero/fingido/não genuíno/ingênuo da parte de alguém (no caso do exemplo 1).

http://www.thefreedictionary.com/cheesy
chees•y   (ch  z )
adj. chees•i•er, chees•i•est
1. Containing or resembling cheese.
2. Informal Of poor quality; shoddy.

http://answers.yahoo.com/question/index?qid=20111201125348AAGoXA7

Cheesy = something that's trying too hard and ends up looking fake
Like "He has a cheesy smile on his face" means he has a fake plastered smile.

http://www.urbandictionary.com/define.php?term=cheesy

1.

 This is an important word and nobody has it right yet. What it means is: Trying too hard, unsubtle, and inauthentic.
Specifically that which is unsubtle or inauthentic in its way of trying to elicit a certain response from a viewer, listener, audience, etc. Celine Dion is cheesy because her lyrics, timbre, key changes, and swelling orchestral accompaniment telegraph 'I want you to be moved' instead of moving you.        Gold chains on an exposed hairy chest are cheesy because they shout out: "I have money and I am manly" instead of impressing a woman in a more subtle way, or allowing a woman to form her own judgments.

  The excessive showing off suggests he's compensating for what he does not have--i.e., he's actually poor, insecure, or short with an inferiority complex. Cliches are often cheesy because they are an obvious and artless way of making a point.     A movie might be cheesy if it contains 'on the nose' dialogue, like "I can't live without you" or "You had me at hello."
   Cheesiness is subjective. What seems cheesy to me, may be a legitimate and attractive hairstyle to you. What seems cheesy to me, may cause you to weep and hug your girlfriend tight.

4.
Cheesy  42 up, 36 down

 Cheesy is a unique word it's usually used for calling something bad but it isn't directly bad. Cheesy means something that is trying too hard to be good, basically something that's supposed to be good but it isn't and bad.
For example, Twilight is cheesy you can see that they are trying hard for the movie to be good but it's just a cheesy vampire story.

Jersey Shore is cheesy because they are trying too hard to be 'cool' while it's just bunch of crap.