My understanding is that creatures with shadow can only block or be blocked by creatures with shadow, and creatures with flying can only be blocked by creatures with flying. If I have a creature with shadow and cast a spell that gives it flying (say, Jump), can it now only be blocked by nothing but a creature that also has both those abilities?
In a general sense, you are correct. Both abilities impose a restriction that's tracked individually. A creature must satisfy all the restrictions in order to block your super-evasive attacker.
My one niggle is that there are non-flyers that can block fliers, such as creatures with reach. And there are a few creatures, like Wall of Diffusion, that don't have shadow but have "~ can block creatures with shadow as though ~ had shadow" as an ability, which allows them to block shadow creatures (and non-shadow creatures as well, since they don't actually have shadow).
Here's some comp rules for ya, with this exact example:
509.1b The defending player checks each creature he or she controls to see whether it’s affected by any restrictions (effects that say a creature can’t block, or that it can’t block unless some condition is met). If any restrictions are being disobeyed, the declaration of blockers is illegal.
A restriction may be created by an evasion ability (a static ability an attacking creature has that restricts what can block it). If an attacking creature gains or loses an evasion ability after a legal block has been declared, it doesn’t affect that block. Different evasion abilities are cumulative.
Example: An attacking creature with flying and shadow can’t be blocked by a creature with flying but without shadow.
Trivia: Stronghold Overseer has both flying and shadow natively. On a 5/5 body to boot!
Yes you need both to fulfill both requirements to be able to block a creature with both shadow and flying. You can fulfill these requirements either by having shadow and flying or through other abilities such as reach.