Can I travel to Romania with a Schengen visa issued by the embassy of The Netherlands and staying for a longer period in Romania than in Amsterdam?

Can I apply for schengen visa from the embassy of The Netherlands?

Not only that but you must apply for a Dutch Schengen visa to go to the Netherlands (if you need a visa to enter the Schengen area, obviously). Romania isn't part of the Schengen area yet and cannot issue a short-stay visa that would allow you to travel to the Netherlands.

Will it permit me to enter Romania?

Some Schengen visas might allow you to enter Romania but not all of them. If you get a single entry visa from the Dutch, you will need a Romanian visa as well. On the other hand, if you are lucky and you get a double entry or multiple entry visa with enough validity, it would exempt you of the Romanian visa requirement.

The catch is that the Dutch are under no obligation (and have no reasons) to accommodate you. Meaning they won't issue a long multiple entry visa because you want to go to Romania, they will only consider the info about your stay in the Netherlands. If you haven't been to the Schengen area before, you will probably get a short single entry visa.

Bottom line: Start by applying for the Dutch visa, there is a slim chance it will be enough but in all likelihood, you will need a Romanian visa too.

Keep a copy of all the documentation to help you prepare the second application, the Romanian visa process should in principle be very similar (as part of their preparation to enter the Schengen area, they had to align their rules and practices to the Schengen rules).

As of now, Romania is not a part of the Schengen area. Coming implementation should be in March, 2015. It is also worth mentioning that this is not the first implementation plan, other ones were delayed before, and it's also worth mentioning not to expect Romania to be part of the Schengen area by March as it is a long process.

Regarding visiting Romania, they still issue separate visas. So, if you plan to apply for the visa now, you should apply for the Romanian visa at a Romanian embassy or consulate, if you are planning to apply later before your visit, then it is better to apply for a Schengen visa in a Romanian embassy to be on the safe side as Romania will be your major stop (if they start issuing Schengen visas in their embassies).

So, you should obtain the Schengen visa from the Dutch Embassy, and apply for a Romanian visa from the Romanian embassy.

If you hold a multiple-entry Schengen visa or a residence permit, you should be able to visit Romania legally for maximum 90 days stay. Read carefully here: Romanian Ministry of Foreign Affairs

Quoting from that site (taken on 2015-02-17):

Can I travel to Romania without a visa if I hold a visa issued by a Schengen Member State?

The holders of Schengen visas with two or multiple entries, of national visas or residence permits issued by Schengen States are not required a Romanian visa to enter, transit or stay on the territory of Romania for 90 days in any 180-day period. Therefore, you can travel to Romania without a visa only if you hold a valid Schengen visa with at least two entries.

ATTENTION! The validity, right of stay and number of entries granted by the Schengen visa you hold should not have been fully consumed! Moreover, you should bear in mind that the right of stay in Romania shall be equal to the right of stay conferred by the Schengen visa (example: if you hold a Schengen visa with a right of stay of 10 days, you will have the right to stay in Romania only 10 days).

According to the immihelp website:

A short stay Schengen visa entitles the holder to visit the Schengen countries for tourism, visiting friends/family, business etc., up to 90 days within a 180 day period from the date of first entry. The stay may be either continuous or several visits depending upon whether the visa is single or multiple entry.

Single-entry visa: Allows uninterrupted stay. Once the person departs the Schengen territory, he/she can't enter again without obtaining a new visa.

Multiple-entry visa: Allows multiple stays in one or more Schengen countries, as long as the total length of the stay does not exceed 90 days in a given 180 day period from the date of first entry. The stay may either be continuous or spread over several visits within the validity periods of the visa, but no more than the number of entries authorized by the visa. A multiple entry visa may be valid for 1 year. If the entries show "02", you are allowed 2 entries. If the entries show "MULT", you are allowed more than 2 entries.

A multiple entry visa is not issued at all the embassies/consulates.

If the validity of the visa is over while visiting the Schengen territory, the person can no longer stay in the Schengen territory even if the person has not stayed for 90 days. Additionally, the visa will expire when the total number of exits made by the visa holder equals the number of authorized entries, even if the visa holder has not used up the number of days authorized by the visa.

Now according to the Romania embassy website, when applying for an E-Visa you will only be allowed entry into Romania if you are holding a multiple entry visa.

As stated by Timatic, the database used by airlines:

Visa required, except for passengers with a double or multiple entry C visa issued by a Schengen Member State valid for the period of intended stay. They are visa exempt for a maximum stay of 90 days

So you can enter Romania with a double or multiple-entry visa, but if holding a single-entry visa (the most common type) you'll need a Romanian visa too.