I don't feel qualified to speak to this question on the whole since I'm not primarily a historian of World War I, but I can answer at least with respect to Romania. Romania was in a complex situation when the war broke out in 1914. The primary geopolitical objective for Romania was the unification of all of the territories inhabited by ethnic Romanians. Romania had been formed in 1859 through the union of the principalities of Wallachia and Moldavia, which formed the core of the state when it officially became independent in 1877. Romania had been on the victorious side of the Balkan Wars, and had received the territory of Dobruja from Bulgaria in 1913 after the Second Balkan War. However, Romania still had designs on the other Romanian-majority regions, namely Transylvania (then part of Austria-Hungary) and Bessarabia and Bukovina (then part of Russia), and acquiring these territories was its primary ambition.

Romania's situation with respect to the Great Powers and, ultimately, the two sides in the war, was complicated. Romania's king, Carol I, was a Hohenzollern, and pursued a pro-German foreign policy. As a result, Romania had been part of the Triple Alliance (along with Germany, Austria-Hungary, and Italy) since 1883. It also had strong economic ties with Germany, which was the primary destination for its oil exports. However, much of the Romanian intellectual and political class, as well as the general public, was Francophile, and more sympathetic to the Entente. When the war began, Romania declared its neutrality, arguing (like Italy) that it had no obligation to intervene on Austria-Hungary's behalf since Austria-Hungary was the aggressor.

Carol died in 1914 and was replaced by his nephew, Ferdinand, who was more sympathetic to the Entente. After Ferdinand came to power, the Romanian government, led by Prime Minister Ion I. C. Brătianu, began secret negotiations with the Entente. Romania knew that it was in a compromised position militarily, surrounded on three sides by members of the Triple Alliance (Austria Hungary in the north and west and Bulgaria in the south), and demanded strong commitments from the Entente powers in order to secure its entry into the war, including not only territorial concessions but also troops and weapons, as well as the creation of a southern front with Bulgaria in Thrace to secure Romania's southern flank. Romania had a large army relative to its size, but lacked the industrial capacity to produce modern weapons on the scale that would be required, so it would need a major commitment in that respect from its allies in order to manage the looming threat of a two-front war.

The Allies gave Romania an ultimatum in August 1916, which put pressure on the Romanian government, which had been waffling on the question of entering the war. In the end, the Romanian government decided that the potential benefits of achieving their territorial aims was worth the risk of fighting a two-front war. They signed the Treaty of Bucharest on 17 August, which committed them to an invasion of Austria-Hungary by the end of the month. The Entente powers had agreed to Romania's territorial demands, although John Keegan claimed that they had already decided amongst themselves that they were going to renege on that agreement after the war.

Romania's battle plan was essentially to commit all of its offensive firepower to a two-pronged assault on Austria-Hungary, with troops advancing through the Carpathians westward from Moldavia and northward from Wallachia, while fighting a defensive action along the southern front if Bulgaria threatened an invasion across the Danube. Romania anticipated the Entente's attack on Bulgaria to tie down their forces, allowing a full-scale commitment to the invasion of Austria-Hungary, which was intended (along with the Russian Brusilov Offensive) to knock Austria-Hungary out of the war and further isolate Germany, which was heavily committed on the Western Front and not expected to contribute much to the defense of Transylvania. The Romanians initially advanced quickly against relatively sparse Austro-Hungarian forces in Transylvania, but contrary to the Romanian expectations, the Germans committed eight divisions under Erich von Falkenhayn, who had recently been relieved of his role as Chief of the German General Staff, and they were able to grind the Romanian advance to a halt by the end of September. Meanwhile, a combined German/Bulgarian/Ottoman force led by August von Mackensen attacked Dobruja; the Entente powers hadn't opened the promised second front, leaving Bulgarian forces free to move against Romania. Romania soon found itself overstretched and facing the precise situation it had feared: a two-front war with virtually no support from its allies. Romanian forces were soon in headlong retreat, and Falkenhayn's men captured Bucharest on 6 December.

However, the Central Powers weren't able to knock Romania out of the war, despite taking the Romanian capital. The Romanian parliament formed a government of national unity based in Iași at the end of December 1916, and Romania continued to put up spirited resistance in 1917, achieving several notable defensive victories in Moldavia. However, after the Russian Revolution, Romania lost its only source of direct contact with its allies and had no choice but to sue for peace, signing an armistice with the Central Powers in December 1917. In May 1918, Romania concluded a treaty with the Central Powers, which granted it Bessarabia from Russia, but also imposed harsh economic and political terms; however, Ferdinand refused to sign the treaty. Romania re-entered the war on 10 November 1918, the day before the armistice went into effect in the west, re-asserting its status as a co-belligerent and launching an invasion of Hungary that lasted into 1919 and eventually toppled Bela Kun's communist regime there. Romania was largely excluded from the Paris peace negotiations and was treated as a minor power rather than as a core member of the Allied Powers. However, Romania ultimately achieved most of its territorial objectives, as it received Transylvania from Hungary in the Treaty of Trianon, while Bessarabia and Bukovina also voted to unite with Romania and Romania retained control of southern Dobruja. These territorial gains formed a state referred to as Greater Romania (România Mare),which represented the maximum territorial extent of the Romanian state. Romania was therefore a sated power, but faced irredentism from virtually all sides, and its revanchist neighbors' determination to regain their lost territory was the driving force behind Romania's foreign policy in the interwar period (and ultimately resulted in the rise of Ion Antonescu and Romania's involvement in World War II).

Sorry, I assume you didn't write this question with the intention of getting information about Romania, but I wanted to stay in my lane and leave the bigger picture to more qualified historians who deal with those matters as their primary subject area of expertise.

Sources:

Michael B. Barrett, Prelude to Blitzkrieg: The 1916 Austro-German Campaign in Romania (Indiana UP, 2013)

Keith Hitchins, Rumania 1866-1947 (Oxford UP, 1994)

John Keegan, The First World War (Alfred A. Knopf, 1998)

Glenn Torrey, The Romanian Battlefront in World War I (UP of Kansas, 2012)