This is my first submitted solution, and I hope I've figured the time
zones right and it's actually been 48 hours. Also, I haven't been
coding Ruby (or at all) for all that long, so I hope my code is
decent.
It was a fun quiz. I had to choose some rules that don't quite match
up with natural speech in my dialect, since I was unable to pin down
systematically what the rules for my dialect are. (I say "nine hundred
one", but "two hundred and one", for instance. It's just odd.)
Anyway, without further ado:

class Integer

  def teen
    case self
    when 0: "ten"
    when 1: "eleven"
    when 2: "twelve"
    else    in_compound + "teen"
    end
  end

  def ten
    case self
    when 1: "ten"
    when 2: "twenty"
    else    in_compound + "ty"
    end
  end

  def in_compound
    case self
    when 3: "thir"
    when 5: "fif"
    when 8: "eigh"
    else    to_en
    end
  end

  def to_en(ands=true)
    small_nums = [""] + %w[one two three four five six seven eight nine]
    if self < 10: small_nums[self]
    elsif self < 20: (self % 10).teen
    elsif self < 100:
      result = (self/10).ten
      result += "-" if (self % 10) != 0
      result += (self % 10).to_en
      return result
    elsif self < 1000
      if self%100 != 0 and ands
        (self/100).to_en(ands)+" hundred and "+(self%100).to_en(ands)
      else ((self/100).to_en(ands)+
        " hundred "+(self%100).to_en(ands)).chomp(" ")
      end
    else
      front,back = case (self.to_s.length) % 3
        when 0: [0..2,3..-1].map{|i| self.to_s[i]}.map{|i| i.to_i}
        when 2: [0..1,2..-1].map{|i| self.to_s[i]}.map{|i| i.to_i}
        when 1: [0..0,1..-1].map{|i| self.to_s[i]}.map{|i| i.to_i}
        end
      degree = [""] + %w[thousand million billion trillion quadrillion 
      quintillion sextillion septillion octillion nonillion decillion
      undecillion duodecillion tredecillion quattuordecillion
      quindecillion sexdecillion septdecillion novemdecillion
      vigintillion unvigintillion duovigintillion trevigintillion
      quattuorvigintillion quinvigintillion sexvigintillion 
      septvigintillion octovigintillion novemvigintillion trigintillion 
      untregintillion duotrigintillion googol]
      result = front.to_en(false) + " " + degree[(self.to_s.length-1)/3]
      result += if back > 99: ", "
                elsif back > 0: ands ? " and " : " "
                else ""
                end
      result += back.to_en(ands)
      return result.chomp(" ")
    end
  end

end

# I'm not really happy about re-defining degree, but I couldn't figure
# out where to put it so it would be available both places I use it.
degree = [""] + %w[thousand million billion trillion quadrillion 
quintillion sextillion septillion octillion nonillion decillion
undecillion duodecillion tredecillion quattuordecillion
quindecillion sexdecillion septdecillion novemdecillion
vigintillion unvigintillion duovigintillion trevigintillion
quattuorvigintillion quinvigintillion sexvigintillion 
septvigintillion octovigintillion novemvigintillion trigintillion 
untregintillion duotrigintillion googol]
medium_nums = (1..999).map{|i| i.to_en}
print "The alphabetically first number (1-999) is: "
puts first = medium_nums.min.dup
first_degree = degree[1..-1].min
first << " " + first_degree
puts "The first non-empty degree word (10**3-10**100) is: "+first_degree
next_first = (["and"] + medium_nums).min
first << " " + next_first
puts "The next first word (numbers 1-999 + 'and') is: "+next_first 
if next_first == "and"
  puts "Since the last word was 'and', we need an odd number in 1..99."
  odd_nums = []
  (0..98).step(2){|i| odd_nums << medium_nums[i]}
  first_odd = odd_nums.min
  puts "The first one is: "+first_odd
  first << " " + first_odd
else # This will never happen; I can't bring myself to write it.
end
puts "Our first odd number, then, is #{first}."