Watford Junction station is in an extension to Zone 9 of the London rail system and served by both Underground (Bakerloo Line) and National Rail (London Midland & Southern) services. Watford High Street station is in Zone 8 and served by the Bakerloo Line only. Those services link into the Underground lines which will get you around all of the main attractions within central London.
As he'll be travelling with you, your 10yo son will travel for free, with no ticket needed. You and your older son will both need Oyster cards or Off-Peak Day Travelcards. If you opt for Oyster cards you'll have to pay the (refundable) deposits on them and charge them up with sufficient credit to cover your travel. You'll also need to get the issuing ticket office to set the 'Young Visitor Discount' on your son's card, so that he can travel at half price:
https://tfl.gov.uk/fares-and-payments/travel-for-under-18s/travelling-with-children?intcmp=25255
For just a couple of days though it would probably be simplest to use One Day Travelcards, especially as the price advantages which normally make it cheaper to use Oyster cards don't apply when travelling in from Watford Junction. (You could actually end up spending more with Oyster because you're charged 'peak' fares from 1600 to 1900 with Oyster but there's no evening peak when using Travelcards).
So if you won't be travelling before 0930 on a weekday, your fares each day will be as follows if you travel from Watford Junction:
You: £17.50
Oldest son: £8.70 (or £2.30 if you've got a Family & Friends Railcard or a Network Railcard)
Youngest son: Free
If you want to include travel before 0930 on a weekday (from Watford Junction),your fares each day will be:
You: £23.00
Oldest son £11.50 (with no discount available if you hold a Railcard)
Youngest son: Free
Travelling from Watford High Street (with no travel before 0930 on a weekday) you'll pay these fares each day:
You: £13.10
Oldest son: £6.50 (or £2.30 if you've got a relevant Railcard, as above)
Youngest son: Free
To include peak-time morning travel from Watford High Street, you'll pay these fares:
You: £22.10
Oldest son: £11.00
Youngest son: Free
You'll see that it's significantly cheaper to travel from Watford High Street (especially at off-peak times) than from Watford Junction but that does force you to use the Bakerloo Line, rather than National Rail services, so it will take you longer to get into central London.
http://content.tfl.gov.uk/adult-fares-2017.pdf
http://content.tfl.gov.uk/11-15-zip-fares-2017.pdf