So nineteen to one is how the dog is priced?

Yes. The odds are too high for Prakash to be interested in. However, "too many odds" is wrong. Odds (an uncountable plural noun) are just odds. Each dog is given its own odds, ("nineteen to one", "three to one", "evens" or whatever). Odds might be "too high" or "too low", or "too long" or "too short". Other adjectives are possible as well, but you cannot use "too many".

I really need some help with the terminology here. Short-odds chances (more obvious bets?). What's an outsider in this context?

Short odds are when you get very little money for a dog winning. Odds of nineteen to one are easy to understand: If you bet $1 and the dog wins, you get back $19 winnings plus your original $1 stake, giving $20 in total. This is a lot of money when there are only six runners, and nineteen to one would be long odds.

At odds of two to one, you would get $2 winnings on a $1 stake. At evens, you win $1 if you bet $1 and the dog wins.

You can also have fractional odds, such as six to four (you win $1.50 for each $1 bet) and five to four (you win $1.25 for each $1 bet). You can also have "odds on" bets, such as "two to one on", where you only win $0.50 if you bet $1 and the dog wins. Every time you also get your stake back, so "winnings" is always profit, but it might not be much profit.

The less you get back in winnings, the shorter the odds. What constitutes short odds or long odds depends on the nature of the race. For dog races with only six runners, average odds are five to one, which is therefore neither long nor short. Short odds in dog racing is probably something less than two to one. Long odds would be something more than about ten to one, and you can say that any dog with odds of more than ten to one is an outsider.

Professional gamblers look for discrepancies between a dog's odds and what they think is its actual probability of winning, and this is the "mispricing" that Prakash mentions. Different gamblers focus on different things. One person might look for dogs priced as outsiders but which have a reasonable chance, and this appears to be what the other person is suggesting to to Prakash. However, this is not how Prakash gambles. He is looking at the other end of the market, perhaps seeing a dog priced at eleven to ten ($1.10 winnings for a $1 bet) which he thinks actually has a 50% chance of winning. There's a 50% chance he'll lose his money, but there's a 50% chance of his ending up with $2.10. It isn't much, but he is looking at small margins, as he indicates by that gesture.