Whenever Jabba says something to Leia in Huttese she never seems confused at all - she seems to understand what he's saying. Also, when Jabba gives Leia an order or talks to Leia, does he do it in Basic or Huttese?
Probably, but not necessarily
While Leia reacts to Jabba directly, there isn't a scene where she is doing so verbally that Threepio is not translating.
From the transcript:
Leia is disguised as Boushh
Jabba continues speaking, as Threepio nervously translates. Boushh listens, studying the dangerous creatures around the room. He notices BOBA FETT standing near the door.
THREEPIO Oh. The illustrious Jabba bids you welcome and will gladly pay you the reward of twenty- five thousand.
BOUSHH (in Ubese subtitled) I want fifty thousand. No less.
Later, Leia may be reacting as much to Jabba's physical actions as verbal ones:
LEIA We have powerful friends. You're gonna regret this...
JABBA (in Huttese subtitled) I'm sure.
Inexorably her lovely face moves to within a few inches of Jabba's ugly blob of a head, and Leia turns away in disgust.
Which is pretty much the last bit of dialogue for her and Jabba. They don't seem to have much to discuss after this...
However, considering the following:
- Leia was a Senator and diplomat and therefore probably knew quite a few languages. She apparently learned Ubese by this point, for instance.
- The Hutts are a powerful business entity in the galaxy, so Alderaan has possibly done business with them.
- Han certainly understands Huttese, so it isn't uncommon for Humans to learn.
It's not unreasonable to assume she understands the language. But from the movies at least, no confirmation that she does.
According to C-canon, Liliac (and Jabba) spoke Basic.
Han bowed again. “Lord Jiliac,” he said, in Basic, “it is a privilege to meet you, Your Excellency. Your cousin Lord Tagta says that you are always in need of good pilots.”
“Pilot Solo”-Jiliac turned bulbous eyes layered in fat upon Han, and peered down at him with faint curiosity-
“do you speak and understand Huttese?” (Clearly, he spoke in Basic as he didn't know if Han understood Huttese)
“I understand it, Your Excellency. I do not speak it well enough to convey the beauty of the language, therefore it is not proper for me to attempt to utter it,” Han said earnestly.
Han bowed to the younger Hutt. “Greetings, Your Excellency.”
“Greetings, Captain Solo,” Jabba replied with a gracious wave of his small hand. “Your reputation precedes you.”
Jiliac held out his own hand. “Enough chitchat. The holocube, Captain?” “Certainly, Your Excellency.” Han produced it, handed it to Jiliac.
(src: Han Solo series Book 2 - The Hutt Gambit)
Please note that if you search for "Huttese" in book, you will see that it's very frequently mentioned that Hutts speak in Huttese specifically in various situations (including to Boba Fett). Therefore, the lack of such clarification here makes me assume it was Basic.
There is no mention of Leia understanding Huttese, though she does seem to understand Jabba's comments. She is never spoken to in Huttese or professed to understand Huttese during the EU. She can speak Ubese, which she uses to speak to Jabba in Return of the Jedi.
Jabba, however, to answer the question put in the comments, is shown to both understand and speak Basic during the EU. Putting aside the two occasions DVK mentions in his answer -as I tend to side with SSumner on this, and did so when I read the trilogy in question years ago, that Jiliac and Jabba are in fact speaking Huttese and assuming that Solo understands as he answers - in Shadows of the Empire, Jabba speaks Huttese to Prince Xizor, who requests that he speak Basic. Jabba replies, in Basic, "as you wish," and continues the conversation in that language.
“According to her diplomatic profile, Princess Leia speaks both Huttese and Shyriiwook fluently. Regretfully, and as Your Majesty is keenly aware, the princess is merely proficient in Shyriiwook. This is, naturally, a failure of mine and not the princess, but I worry that such an error might cause her embarrassment. Oh, it is too, too humiliating.”
Breha allowed herself a smile and turned, putting a motherly hand on the droid’s shoulder. “It’s hardly your fault that Leia did not apply herself more rigorously. I wouldn’t worry. I’m struggling to imagine a scenario in which fluent Shyriiwook would benefit her.” The droid’s eyes flickered, brighter, as if in shock. “On this particular mission, of course,” the queen quickly added.