Teddington and Strawberry Hill are much smaller areas than Kingston, and more homogenous. They are very affluent, good schools, low crime etc. They are both lovely (and very close each other); my main preference for Teddington (where I live) is because it has a better high street than SH - more of a centre - and that is important to me.
Kingston covers a much larger area and is more mixed. There are very posh bits and not so posh bits. Also loads of good schools. Big shopping centre, great shops, much more urban and busy feeling, more rough on a Saturday night. More racially and socially diverse, more vibrant.
So I think that you will find Kingston properties that are cheap relative to Teddington and Strawberry Hill, but also properties that are just as expensive.
Twickenham is up the road from Strawberry Hill. it is more of a centre, but not as good shopping as Kingston. Some nice bits, but it's not to my taste as much as the other areas. However, it does have a much quicker train line into central London.
USP of each of them, summed up:
Kingston: great shopping, great schools, grammar schools if that's your thing, some lovely parts, nightlife
Twickenham: 20 minutes into Waterloo, some good schools, some lovely streets and houses
Teddington: smaller and quieter, nice high street, great schools, good community atmosphere, very safe feeling, you'll want to get within the catchment of Teddington School for secondary
Strawberry Hill: smaller and quieter still, some lovely huge houses if you can afford them, great primaries, if you have daughters you'll get them into Waldegrave School which is considered fantastic