First, there are physically impossible double stops. The notes below the open next-to-lowest string can only be played on the lowest string, so you can't play two notes at a time in that range. For example, a low G-B double stop on violin would be impossible.
Next, understand how the instrument is tuned. Viola, violin, and cello are tuned in fifths, while the bass is tuned in fourths. This means that those intervals require zero reach, and as the interval grows or shrinks from there it requires the player to stretch further.
The limitation then comes from the scale of the instrument, and that the notes are furthest apart in the lowest positions (closest to the nut). On violin and viola, reaching up to an interval of a fourth (on one string) is basic technique in any position, meaning that double stops from a major second to an octave are natural. There are solo violin excerpts stretching up to a tenth, but that should be considered advanced.
On cello, as another commenter explained in more detail, the reach is more limited so you should stick to thirds and sixths more. The span involved in reaching minor or major sevenths is the same as for major or minor thirds (respectively), but the seventh is a dissonant interval so it's rarely seen. Seconds and octaves should be considered advanced.
On contrabass, the scale is so large that you can't reach very far at all. To give you an idea: on a 3/4 size bass I can barely span a whole step in first position, and I can easily reach a tenth on piano. Remembering that the strings are tuned in fourths, the limit for double stops in low positions is merely from thirds to fifths. Considering that small intervals sound muddy in the bass register, you should probably only ever write fifths, if even that.
When writing phrases containing consecutive double stops, it's always easiest when the span is comfortable and the notes move in parallel. For violins and violas, consecutive thirds and sixths (even mixing major/minor) are very common. Consecutive octaves are a bit more advanced but still considered standard. Of course, the other intervals are also possible but compositionally questionable. You won't see runs like this on cello as much, but consecutive sixths are very playable.
When writing phrases consisting of consecutive double stops of varying intervals, there are all sorts of pitfalls you can fall into, and it's hard to summarize them in a post like this. I might suggest that such writing is best left to advanced players of these instruments, or at least you should check the parts with a player rather than trying to apply some general rule.