[Firehchicken]

I understand that a strong nucleophile is also a strong base, but I am unable to understand why A) is the strongest base among the 4.

I am guessing it has something to do with the hybridisation but I cannot see exactly why A) is stronger compared to B).

Isn't the oxygen in B) sp3 hybridised whereas A) is sp2 hybridised, and therefore B) should be the stronger base?

[Babcock_Hall]

Although there is often a correlation between nucleophilicity and basicity, there are other factors that come into play.  Nucleophilicity is a kinetic phenomenon; in other words a strong nuclephile is one that reacts quickly.  Does that help?

[Firehchicken]

Although there is often a correlation between nucleophilicity and basicity, there are other factors that come into play.  Nucleophilicity is a kinetic phenomenon; in other words a strong nuclephile is one that reacts quickly.  Does that help?

Hmm so in other words compound B) is more stable than A)... but how?

[NateDogg]

Ready nucleophillic attack requires sufficient electronegative character, as well as physical access to the recipient electrophile. Does this help?

[Firehchicken]

Ready nucleophillic attack requires sufficient electronegative character, as well as physical access to the recipient electrophile. Does this help?

So compound A) is less sterically hindered than compound B). Right.

[Babcock_Hall]

Although there is often a correlation between nucleophilicity and basicity, there are other factors that come into play.  Nucleophilicity is a kinetic phenomenon; in other words a strong nuclephile is one that reacts quickly.  Does that help?

Hmm so in other words compound B) is more stable than A)... but how?

I use the term "stability" when I am talking about thermodynamics.  Your subsequent answer, steric hindrance, is correct.